( 



7\sn\ 



A TREATISE ON THE PLANE-TABLE 



AND 



ITS USE IN TOPOGEAPHICAL SURVEYING. 



[PROM THE COAST SURVEY REPORT FOR 1865. 



/ 



4 ' 



> 



Z. 



A TREATISE 



ON 



THE PLANE-TABLE 



AND 



ITS USE IN TOPOGRAPHICAL SURVEYING. 



[FEOM THE COAST SUBVEY EEPOET FOE 1865. J 



WASHINGTON: 

GOVERNMENT PRINTING OFFICE. 
1 870. 



f v 



JUN 
O.otO. 



A x 



^v 




X >J 



( 



TREATISE ON THE PLANE-TABLE AND ITS USE IN TOPOGRAPHICAL SURVEYING. 



[Introductory note. — The plane-table is used iu the Coast Survey as the principal instrument for mapping the 
topographical features of the country, and is universally recognized as the most efficient and accurate means for that 
purpose. Its application under various conditions, the methods of its use, and styles of topographical representation, 
have received a great development in the practice of the topographers of the Coast Survey, and special acknowledg- 
ment is due in this respect to the comprehensive views, practical tact, and elegant taste of Assistant H. L. Whiting, 
whose efforts have established the high standard of topographical maps recognized in the Coast Survey. In order to 
meet the frequently expressed want of a treatise on the plane-table and its use, which does not appear to be supplied 
by any existing book in our language, the following essay has been prepared for this report by Assistant A. M. Harrison, 
who acknowledges his indebtedness to many of his colleagues for contributions and aid in its preparation. The chapter 
on the three-point problem has been supplied by Assistant E. Hergesheimer.] 

The following description of the plane-table, as now used in the United States Coast Survey, 
and directions for its use, are given after a long test of its qualities on that work. Being the 
instrument best adapted to topographical field-work, the very inadequate notices given of it in 
most American and English works make it desirable to furnish topographical surveyors with a 
practical manual of its use. This paper may seem in some cases somewhat amplified, but those 
more familiar with the instrument wiil overlook details intended for the benefit of beginners. 

The invention of the plane-table is ascribed to Prsetorius in 1537, but the first published 
description appears to be that of Leonhard Zubler, in 1625, who ascribes the "beginning" of the 
instrument to one Eberhart, a stonemason. •« From this time forward it has received successive 
improvements, chiefly from the Germans and French, until it has reached its present form, which 
is sufficiently perfect for the nicest accuracy required in an extended topographical survey. 

Topography is that branch of surveying by which any portion of the land surface of the 
earth is mapped in plan on a specified scale or proportion of nature. With the plane-table such a 
map is constructed on the ground by at once drawing upon the paper, which is spread upon the 
table, the angles subtended by different objects, and determining by intersections their relative 
positions, instead of reading off the angles on graduated instruments and afterward plotting the 
lines by means of a protractor, as is done in other methods of surveying. The practice with the 
plane-table has in this respect a great advantage in directness and precision. The measurement 
of distances and of vertical angles are used, in conjunction with the method of intersections, 
to obtain all the data for representing the horizontal and vertical features on the map, which is 
drawn in the field with pencil, the details being filled in according to established conventional signs. 

The plane-table of the Coast Survey (see Sketch No. 30) is composed of a well-seasoned 
drawing-board, with beveled or rounded edges, about thirty inches in length, twenty-four in 
width, and three-quarters of an inch thick. It is commonly made of several pieces of white pine, 
tongued and grooved together, with the grain running in different directions to prevent warping. 
It is supported upon three strong brass arms, to which it is fastened by screws passing through 



4 TEEATISE ON THE PLANE-TABLE, 

them and entering the under side of the board, the three holes for the reception of the screws 
being guarded by brass bushings, and situated equidistant from each other and from the center of 
the table. By means of these screws the board can be removed at will. The arms rest upon the 
sloping upper face of a conical plate of brass, to which they are permanently fixed. Upon its 
lower edge or periphery this cone is fashioned into a horizontally projecting rim, the inferior face 
of which is as nearly as possible a perfect plane, and this in its turn rests upon a corresponding 
rim of a somewhat greater diameter projecting slightly beyond it. This second rim forms the 
upper and outer flange of a circular metal disk in the form of a very shallow cylinder. The inferior 
face or plane of the upper flange or rim has, at its contact with the superior face of the lower, a 
horizontal rotary movement about a common center, which is the center also of the instrument, 
and the two are held together by means of a solid conical axis of brass extending upward from 
the center of the inner face of the lower disk. A socket of similar shape fits exactly over this axis, 
projecting downward from the inner side of the apex of the conical or upper disk. The two plates 
are held together by means of a mill-headed screw capping the cone from the outside, and which 
can be loosened or removed at pleasure. 

A tangent screw and clamp fastened to the edge of the upper rim permit, when loose, the 
revolution of the table about its center, and, when clamped to the lower limb, hold the table firm 
while the tangent screw gives a more delicate movement. 

Three equidistant vertical projections of brass, grooved on the under side, and cast in one 
I>iece with the under face of the lower disk, extending from the periphery toward the center, rest 
upon the points of three large screws which come through a heavy wooden block below. This 
block, which is the top of the stand and is approximate in form to an equilateral triangle, is made 
of three pieces or horizontal layers, and is two and a quarter inches thick and very strong. 

The three screws last mentioned have large milled heads, are quite stout, and play through 
the block from below by means of brass female screws let into it. They are the leveling screws of 
the instrument, and are equidistant from its center. 

Upon the under side and center of the lower metal disk is a socket containing a ball with a 
brass arm, which projects through the center of the block from beneath. The lower end of the 
arm is threaded, and upon it plays a female screw with a large milled head, which can be relaxed 
or tightened at pleasure. This screw clamps the whole upper part of the instrument to the stand; 
it is loosened only before leveling, and kept securely clamped at all other times. 

The block is supported upon three legs, and with them forms the tripod or stand of the instru- 
ment, the legs being of such a length as to bring the table to a convenient height for working, 
and so arranged as to be taken off at will, or closed so that their iron-shod and pointed ends can 
be brought together or moved outward, as may be required. For lightness the legs are generally 
made open through the middle of their length, though sometimes they are solid, and each one is 
fashioned at the top into a cylindrical form with an outer flange, the cylinder fitting into a groove 
on the under side and near the edge of a truncated vertex of the block. The flange, by coming in 
contact with the lower edge of the block, prevents a too great spread of the legs. A brass screw, 
connected at right angles with the middle of a movable bolt which runs through the axis of the 
cylindrical head of the leg and projects through a hole in the block, is fastened above by a female 
screw with a large milled head. 

A pair of compass sights or a watch telescope has sometimes been attached to the under side 
of the board of the plane-table. When the table has been put "in position," the watch telescope 
is directed to some well-defined object, and by after reference to it any movement which may have 



AND ITS USE IN TOPOGEAPHICAL SURVEYING. 



taken place out of position in the table during its use can be detected and adjusted. This, how- 
ever, is but a complication of the instrument, and the same purpose can be more readily served by 
the alidade itself. The watch telescope has not been used in Coast Survey work. 

Boilers have been attached to the under side of the table, taking the place of clamps for hold- 
ing the map in its place; but these are very liable to get out of order, and are not regarded with 
favor by the best topographers. 

The alidade consists of a brass rule about twenty-two inches long, having a circular level on 
its upper face. Near the middle of the rule is a perpendicular cylindrical column of brass, called 
the "standard," surmounted by two square brass plates joined by screws, and supporting, horizon- 
tally, a conical journal, through which extends a closely-fitting cone of brass, coming from and 
attached to the side of the telescope. This cone forms the axis of the vertical movement of the 
telescope, and is secured at the extremity by a screw which holds it in its place. The telescope 
itself has the usual cross-hairs and means of focal adjustment. 

A transverse level is fastened to the edge of the upper of the two plates at the top of the 
standard by means of adjusting screws. 

The telescope is so placed that its line of collimation is above and in the same vertical plane 
with the fiducial edge of the rule, though this is not absolutely necessary. Its position with 
regard to the edge should, however, be constant. 

A vertical arc, with a tangent screw and clamp, is attached to the telescopic side of the lower 
brass plate, and, with a vernier which moves in arc as the telescope is raised or depressed, is used 
in the measurement of vertical angles for heights. 

A small strip of brass is sometimes attached by means of horizontal hinges to the edge of the 
rule, after the manner of the ordinary parallel rule, for the purpose of obviating the necessity of 
watching the exact contact of the edge of the rule with the point while sighting; but as it requires 
accurate hinging, which is subject to wear, it has not come into general use. For reconnoissance 
for military purposes it is valuable. 

A declitiatoire, consisting of a rectangular metal box containing a magnetic needle and graduated 
arcs, the north and south line of which is parallel to the outer straight edge of the box; a scale of 
equal parts of brass or German silver ; a set of metal clainps for fastening the map to the table ; a 

pair of sharp dividers ; India-rubber, pencils, and a pen-knife, complete the list of essentials for prose- 
cuting plane-table work. 

Since writing the foregoing description of the alidade, it has been somewhat modified and 
improved. (See frontispiece.) The telescope, instead of being supported on the side of the standard, 
is " transit mounted," resting upon an axis which is supported at either end upon a cross-piece of 
brass, upheld by two square columns, having their bases upon a square plate forming the top of the 
standard, the support and standard being firmly united. This arrangement brings the center of 
gravity over and coincident with that of the standard, instead of outside of it, as heretofore. 

The vertical arc is better protected by being placed inside of the two square uprights, and the 
tangent screw made more stable by being made to play through one of the uprights on the oppo- 
site side from the arc. 

An arrangement for attaching a riding level to the telescope, and the declinatoire being per- 
manently fastened to the rule, are also improvements upon the old pattern. 

Adjustments. — From the nature of the service in some sections of the country the plane-table 
is often necessarily subjected to rough usage, and. there is a constant liability to a disturbance of 
the adjustments ; still, in careful hands, a well-made instrument may be used under very unfavora- 



. 



ble conditions for a long time without being perceptibly affected. One should not fail, however, to 
make occasional examinations, and while at work, if any difficulty be encountered which cannot 
otherwise be accounted for, it should lead directly to a scrutiny of the adjustments. 

1. The fiducial edge of the rule. — This should be a true, straight edge. Place the rule upon a 
smooth surface and draw a line along the edge, marking also the lines at the ends of the rule. 
Eeverse the rule, and place the opposite ends upon the marked points, and again draw the line. If 
the two lines coincide, no adjustment is necessary ; if not, the edge must be made true. 

There is one deviation from a straight line, which, by a very rare possibility, the edge of the 
ruler might assume, and yet not be shown by the above test ; it is when a part is convex, and a part 
similarly situated at the other end concave, in exactly the same degree and proportion. In this 
case, on reversal, a line drawn along the edge of the rule would be coincident with the other, though 
not a true right line; this can be tested by an exact straight edge. 

2. The level attached to the rule. — Place the instrument in the middle of the table and bring the 
bubble to the center by means of the leveling screws of the table ; draw lines along the edge and 
ends of the rule upon the board to show its exact position, then reverse 180°. If the bubble remain 
central, it is in adjustment ; if not, correct it one-half by means of the leveling screws of the table, 
and the other half by the adjusting screws attached to the level. This should be repeated until the 
bubble keeps its central position, whichever way the rule may be placed upon the table. This pre- 
supposes the plane of the board to be true. If two levels are on the rule, they are examined and 
adjusted in a like manner. 

Great care should be exercised in manipulation, lest the table be disturbed. 

3. Parallax. — Move the eye-glass until the cross-hairs are perfectly distinct, and then direct the 
telescope to some distant well-defined object. If the contact remain perfect when the position of 
the eye is changed in any way, there is no parallax ; but if it does not, then the focus of the object 
glass must be changed until there is no displacement of the contact. When this is the case, the 
cross-hairs are in the common focus of the object and eye-glasses. It may occur that the true focus 
of the cross-hairs is not obtained at first, in which case a readjustment is necessary, in order to see 
both them and the object with equal distinctness and without parallax. 

4. To make the line of collimation perpendicular to the axis of revolution of the telescope, and the 
axis of revolution parallel to the plane of the rule. — The instrument is set up and carefully leveled, 
and the cross-hairs directed to a plumb or other vertical bne. If the cross-hairs cover the line 
when the telescope is elevated and depressed, the adjustments are perfect; should they deviate, 
however, from the vertical line, this error may be attributable to two causes : 1st, the line of colli- 
mation is not perpendicular to the horizontal axis ; or, 2d, the axis is not horizontal, and conse- 
quently not parallel to the plane of the rule. In the first case the motion of the cross-hairs will be 
in a curve, and upon being made to cover the vertical line when the telescope is horizontal, will 
deviate from it to the same side both upon elevation and depression. In the second case the move- 
ment of the cross-hairs will be in a straight line oblique to the horizon, and, when made to cover 
the vertical line when the telescope is horizontal, they will, upon being elevated and depressed, 
appear upon different sides of the vertical line. These two cases will be considered separately. 

When the construction of the telescope admits of it, the perpendicularity of the line of colli- 
mation to the axis may be examined as follows : Direct the cross-hairs to a well-defined, distant 
object, as nearly upon a level with the telescope as may be, draw a line along the fiducial edge ; 
then reverse the rule 180°, again placing the edge along this line, revolve the telescope upon its 
axis and again observe the object ; if the cross-hairs cover it, the adjustment is perfect; if not, one- 
half the error must be corrected by moving the cross-hairs by means of the adjusting screws of the 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 7 

diaphragm, and the other half with the tangent screw of the table, and the operation shonld be 
repeated until the adjustment is complete. 

In using the method just given, it may be taken for granted that the line of collimation 
revolves in the vertical plane of the fiducial edge, as any error arising from this not being the case 
would be inappreciable. 

After this adjustment the horizon tality of the axis should be examined. Direct the cross-hairs 
to a distant, well-defined, elevated or depressed object, having the table carefully leveled ; draw a 
line along the fiducial edge, reverse the rule, and again direct toward the object ; if the cross-hairs 
cover it, the axis is horizontal ; if they do not, one-half of the deviation should be corrected by 
means of the screws attaching the upper plate to the top of the standard, or by means of the 
screws attaching the standard to the rule. The level attached to the axis should then be made 
central. In the alidades, as recently improved, the bearings of the axis being unchangeable, save 
by such violence as would destroy the instrument for all practical purposes, the foregoing adjust- 
ment and the succeeding one are, of course, unnecessary, as the instrument is to be considered as 
in constant adjustment in these respects. 

5. To make the line of collimation parallel to the vertical plane of the fiducial edge.—'The exact 
parallelism of these is not necessary, but it is essential that the deviation should remain constant. 
This adjustment may be examined by means of two needles stuck in the table. The table is turned 
so that the needles sight exactly to some distant object; the fiducial edge is then placed against 
them and the telescope directed to the object. If the cross-hairs bisect it, the adjustment is correct; 
but if they do not, it can be corrected by means of the screws attaching the standard to the rule. 

6. Zero of the vertical arc. — When the line of sight is horizontal, the vernier of the vertical arc 
should read 0°, or the index error should be known. This may be examined by means of the distant 
sea horizon, or by setting up the alidade so that the center of the telescope is in the line of sight of 
an accurately adjusted leveling instrument, and then directing both instruments, while level, to a 
distant object ; if any error be discovered, it may be corrected by setting the vernier at 0°, and 
adjusting the horizontal wire to the sea horizon or object. 

When the above means are not available, the following method may be used : Set up the instru- 
ment at a point, measure the angle of elevation or depression of a distant object, remove the 
instrument to that object, and measure the angle of depression or elevation of the first point. 
These angles should be equal if the adjustment be correct ; and if not equal, the index error will be 
one-half the difference of the two readings. 

The following method of making this adjustment, where you have neither a separate level, a 
sea horizon, nor an elevation, may be employed : Set up the table and level it carefully on any level 
piece of ground between two equidistant points A and B, say 600 or 800 meters apart. Determine 
with the table the difference of level of these two points, and remove the table to A. Measure 
carefully the distance from the ground to the center of the axis of the telescope, and add or sub- 
tract this from the difference of level of the point B, according as it is lower or higher than A. Set 
up a target or distinct point at this height at B, direct the cross-hairs upon it, and correct the ver- 
nier accordingly. 

A longitudinal riding level placed upon the telescope, or a level permanently fastened upon the 
top of the telescope parallel to the optical axis, and adjusted to the horizontal wire, will give the 
error at once. 

Plane-table. — With regard to the plane-table proper, a disturbance of its good working condition 
generally arises from accidents resulting from carelessness or from undue exposure of the board to 
the inclemency of the weather, and where these injuries are of a serious nature the mechanician 



8 TREATISE ON THE PLANE-TABLE, 

only can apply the proper remedies. A coating of shellac has been suggested, whereby the shrink- 
age and warping of the board is said to be prevented "in a very marked degree;" but well-seasoned 
wood and fidelity in construction must be the main reliance of the surveyor. 

Paper. — In addition to the faulty adjustment of his instrument the topographer has an addi- 
tional source of error to guard against, arising from the expansion and contraction of the paper, 
due to its hygrometric nature. From the exposure to which a sheet is subject while in use in the 
field, and the occurrence of almost unceasing atmospheric changes, it can hardly ever be considered 
for any great length of time as fixed in its relative proportions ; and the difficulty is greatly increased 
from the want of uniformity in this variation in the different parts of the sheets and in different 
directions. 

In case of trouble with the points arising from this cause, there is but one remedy, and that is 
by the system of compensation as treated of in the article on field-work. 

When points are determined by intersection, the effect of contraction and expansion may be 
uniform enough to be comparatively unimportant ; but in running long traverses without side checks 
it is always felt. 

In plotting long measured distances, the most feasible method of correction is to measure a 
minute of latitude near the place of plotting ; and as the lengths of all these minutes on the sheet is 
the same, a comparison with the scale can at once be made and the percentage of error determined. 
When the sheet has no projection, squares constructed to scale upon it will answer the same 
purpose. 

Scales. — The very simple and ingenious decimal system of scales for maps adopted by the 
French is that in use by Coast Survey. In this system the scale of any map is represented by a 
fraction whose numerator is unity and whose denominator is some multiple of two or five, as 20000? 
iooo"o? soVo? Woo? meaning that any distance on the map is one twenty-thousandth, one ten-thou- 
sandth, &c, of its actual dimensions on the ground. Thus, on a scale of T ojroo> 0Iie decimeter on 
the map will represent an actual distance of 1,000 meters. 

Any other desirable scale can, of course, be used, as a given number of inches to a mile ; and 
in case of triangulating from a base, as in a reconnoissance, no scale, even, need be adopted. By 
assuming two points on the sheet as the extremities of the base, and working from them, a correct 
delineation of the country can be obtained before the base has been measured. After measurement 
the scale of the map can be ascertained by dividing the length of the base on the map by its length 
on the ground, both expressed in the same unit. 

In those regions where there is much detail, T5 i^ is the scale generally used for field-work, 
while in others, where there is but little minute work, 2o^ So - is employed. Less than the latter is 
never used for field sheets. In some cases, such as surveys of cities, wharves, &c, 5 0V0? or larger, 
may be used ; and in surveys for the location of batteries, the mapping of forts, navy yards, sites 
for light-houses, &c, scales as large as y^g- have been used to advantage. 

The diagonal scales of equal parts used on the Coast Survey with the plane-table, for the pur- 
pose of plotting measured distances, correspond with the scales of the maps. They are of metal, 
and sufficiently hard to stand long wear from the points of the dividers. 

Projections for field-work. — The conical projection is that used in the Coast Survey for 
field-work. 

The orienting of the sheet is determined by various considerations. It should include as many 
triangulation points as possible ; it should duly conform to the position of sheets already surveyed 
in the same neighborhood ; and it should embrace the area of the proposed survey in the manner 
most convenient for work, and most effective for the artistic appearance of the sheet when finished. 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 9 

A sketch giving the triangulation points and the approximate shore line comprised in the area 
to be surveyed, being before the draughtsman, he proceeds as follows : 

The limits of the sheet having been determined, the middle meridian A (see appended sketch) 
is located and drawn, and its intersection with the most central parallel determined, at which point 
the perpendicular B is erected. 

The number of minutes of latitude on the central meridian, above and below the central par- 
allel, being known, take the corresponding distance from Table VI, "Projection Tables," C. S. 
Eeport, 1853, Appendix Xo. 39, from under the head " Meridional Arcs," and lay it off (C) above 
and below the central parallel ; and with the same distance as radius, strike arcs DDDD above 
and below from near the extremities of the perpendicular B. With a well-tested straight edge 
draw lines E E through the north and south minutes on the central meridian, and tangent to the 
two arcs D D, to the right and left. This gives three parallel lines perpendicular to the central 
meridian. 

From the same Table VI, from under the head " Lengths of Arcs of the Parallels," take out 
the value corresponding to the number of minutes of longitude, east and west of the central merid- 
ian, and lay off the whole distance F F' F" on each perpendicular, taking each distance from its 
appropriate latitude. Subdivide these into minutes G G' G". 

For the areas usually covered by plane-table sheets the corrections X, for determining the 
abscissas from the arcs of parallels, (Table VI, head u Co-ordinates of Curvature,") are inapprecia- 
ble, and may be disregarded ; the ordinates Y only being used. These give the distances to be set 
off from the lines B and E, perpendicularly toward the pole, for each minute of longitude counting 
from the central meridian. For ordinary field projections of scale T ooqo ^ ne ordinate of the extreme 
minute only need be used, and the parallel drawn a right line from the point so found to the cen- 
tral meridian. This ordinate H being set off on each of the parallels, the meridians are all drawn 
in with a fine ruling pen, then subdivided into minutes, and the parallels carefully ruled in through 
the points of subdivision. 

The projection is verified by applying the measure of a number of minutes of latitude and 
longitude, and by a comparison of diagonal measurements on different parts of the sheet. 

All measurements should be carefully taken from the scale with a keenly pointed beam-com- 
pass, and the marks pricked in the paper should be as light as possible to be seen, so as to insure the 
greatest possible accuracy. 

The draughtsman is supplied with a list of triangulation points, which gives their relative dis- 
tances, their latitudes and longitudes, and also the equivalents in meters of the seconds of latitude 
and longitude, according to which the points are now plotted on the sheet by measuring from the 
corresponding minutes. Thus in the diagram the distance J represents the seconds of latitude; K, 
the seconds of longitude of the trigonometrical point. 

The accuracy of the plotting is tested by a measurement of the respective distances between 
the points with a beani-coinpass, these distances being also given. The latitude and longitude are 
then plainly marked, usually on the north and east sides of the sheet, at one extremity of each 
parallel and meridian, and the pencil marks erased. 

It sometimes becomes necessary to base topographical work upon a detached scheme of trian- 
gulation, before the usual astronomical observations have been made. In this case the only ele- 
ments given are the distances from the points to two projected arcs of rectangular co-ordinates, 
(which are asumed,) and the distances between the points. The projection for plotting these con- 
sists simply of axes of X and Y, so laid on the sheet that it will embrace all the points required by 
A 22 2 



10 TEEATISE ON THE PLANE-TABLE, 

the surveyor, and in the manner most convenient for his work ; and the points are plotted from 
these by the intersection of two arcs with the distances of the points from the axes as radii, either 
north or south, east or west, of the lines of X and Y, as the plus or minus signs given may indicate. 
The only test is by the distances between the points, and there should be at least two from each. 
If the work be correctly done, a conical projection can be constructed on the sheet after it is finished 
and the required astronomical work is completed. 

Should it become necessary to make a topographical survey, when neither the data for projec- 
tions nor co-ordinates nor table of sines and co-sines are at hand, plotting by distances is the only 
recourse left, and great care is absolutely necessary. 

It has sometimes been found expedient to carry on a plane-table survey in advance of the tri. 
angulation, or where the triangulation has not yet been connected with a base. Under such cir- 
cumstances it is advisable to draw squares of any specified number of meters on the sheet, by 
means of which the projection can ultimately be laid down correctly. 

Field-work. — General remarks. — In organizing a party for field-work it is necessary to have 
one man to carry the table. His duty is to remain constantly with the instrument, to leave it under 
no circumstances ; and while the topographer is at work he holds the shade to protect the chart 
from the glare of the sun. In some sections the labor of carrying the table is quite fatiguing, in 
which case another man should be employed with the shade. He should also keep the pencils 
sharpened, and sometimes, when a careful person, he levels the table, thus giving the topographer 
an opportunity to glance over the surrounding country. He should always have with him a spare 
piece of rubber, and one or two extra pencils. Two chainmen are needed, and two or three other 
men with signals, hatchet, telemeter, and other working apparatus to execute various offices, as 
they may be required. The maximum number necessary for field-work in a plane-table party on 
land is five hands, and when using a boat, six. Satisfactory work has been done, however, with 
three, and on very rare occasions with even two men ; but, of course, with less facility. More than 
five and an aid, when but one table is used, is unnecessary, and a less number is a detriment to 
rapid execution. 

The alidade is carried from station to station by the chief of party, resting on the bend of his 
arm, or hanging easily at the side, and in handling is to be seized by the lower part of the standard, 
never by the telescope or rule. Some topographers prefer to have it transported in the box by one 
of the men, and handed to them when the table is set up at a station. It usually weighs 8£ pounds ; 
and there is a fear of its being put out of adjustment or injured by falls on rough ground, or in 
crossing insecure fences, if carried by hand, and a relief is afforded to the arm by being freed for a 
while from its weight ; but one soon becomes inured to the weight so as to feel but little incon- 
venience from it, and carelessness in taking out and replacing it in the box so many times during 
the day is quite as likely to disturb its adjustments, as is also the fall of the box, or rudely setting 
it on the ground. The meter scale is best fastened under the clamps which hold the paper to the 
table, where it is close at hand ready for reference. It has been suggested that it would be an ad- 
vantage to have it engraved upon the rule of the alidade, and it has also been proposed to have 
the scale drawn upon the sheet, and thus afford a correction of error of shrinkage, but its constant 
use would soon seriously deface the paper. The pencils, dividers, and India-rubber can be carried 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 11 

in an outside breast-pocket, the points of the dividers, when not in use, being thrust into the rub- 
ber. A little metallic pencil-holder, pinned upon the left breast of the coat, is used by some sur- 
veyors for this purpose. A handy and compact arrangement for carrying the scale, pencils, &c, is 
a russet leather case 10£ by 2f inches. It is made large enough to accommodate, on the opposite 
sides of the scale, when it is in, three or four pencils, and the dividers protecting the points of both; 
the whole carried in a leather pouch 11 bj r 4£ inches, slung over the shoulder, the pouch accommo- 
dating also note-books for sketching, table of heights, extra pencils, and rubber ; everything being 
at hand and well protected. When the table is set up, the dividers and pencils are taken from the 
case and laid upon the table, and the scale drawn out as needed. Some topographers object to 
carrying the scale upon the table under the clamps, because it is liable to soil the paper, to drop 
out in passing from station to station, is not always in the most convenient place for use, and some- 
times interferes with the play of the alidade. 

It is Veil to have ready a light India-rubber cloth cover to slip over the board in case of a 
sudden shower, as well as to protect the paper from the dust on the roads, mud in swampy ground, 
or water where a boat is used in going from one station to another. The sides of the sheet, where 
they are turned under the table and come more or less in contact with the coat of the observer, 
should be protected by strips of paper about four inches wide, and six inches longer than the side 
of table, so as to fold under it and clamp on with the sheet itself. A plan followed by some topog- 
raphers is to cover the whole sheet as exposed on the table with thin paper, tearing it away at 
those points only where they are at work, and covering again by pasting on patches as soon as 
finished, thus protecting as much of the sheet as possible; but in determining points by forward 
intersections this is impracticable. 

The plane-table must never be rudely handled, never roughly set on the ground, nor carried 
heedlessly through woods or swamps ; and the weight of the body or arms should never rest upon 
it. Instructions should be given the men that, under no circumstances, except in cases of threat- 
ened danger, should the table or instruments connected with it be touched during the temporary 
absence of the topographer. 

Preliminary work. — As an indispensable preliminary to the operations of field-work, the 
topographer must assure himself of the correctness of the plotted points on the sheet, by an 
examination of them in the field, either by actual occupation of each one, or of a sufficient 
number to embrace them all in two or more lines of observation. When this has been done, and 
the points found correct, or properly adjusted, in the manner hereafter described, the regular 
survey is commenced. 

When the determined points are too widely separated to supply, for all portions of the area to 
be mapped by the topographer, a sufficient number for good determination of position, it becomes 
necessary to determine others with special care by the plane-table. This is generally best done as 
the work progresses, and as the topographer develops his wants for points in the execution of 
details. 

Sometimes, from lack of natural objects, it is found advisable to go beforehand over the coun- 
try and locate signals in suitable points for subsequent determination and use. In the location of 
signals, either as permanent points or simply for temporary forward lines, a great deal depends 
upon the good judgment of the person placing them. Two purposes are to be subserved : first, 
the seeing of sufficient known points to give a good determination; and, second, to command a 
view of as great an area of country, and as many natural and artificial features for filling in the 
topography as possible. It should be remarked, also, that in the course of prosecution of the reg- 



12 . TEEATISE ON THE PLANE-TABLE, 

ular work, no favorable opportunity must be allowed to escape for locating a signal or determining 
a point which may at some future time be of service. Advantage should be taken of open places 
in the woods exposing roads or ravines. Piers or draws of bridges, or piles, giving lines up and 
down streams, with precipitous or bluffy and woody banks; trees of unusual appearance in promi- 
nent positions, or bearing flags placed upon them for the purpose; points of rock, off-shore or 
otherwise; lightning-rods, cupolas, weather-cocks, chimneys of factories, and other peculiar and 
marked objects come within this category. In fact, it may be set down as a rule, that well- 
determined signals located at convenient distances over the sheet are more likely to be too few 
than too frequent. 

Signal poles should be straight and perpendicular, the flags upon them adapted in color to the 
background against which they will be seen when observed upon, and be protected from cattle in 
settled districts by stones piled or earth thrown up around their bases. They shoidd also be well 
marked with pegs, or by measurements to neighboring permanent objects, so that in case they are 
disturbed their positions may be found. 

It is taken for granted that some facility in the manipulation of the table is already arrived 
at, as well as a knowledge of conventional topographical signs (see Sketch No. 32) and the appli- 
cation of them. On maps of a large scale, it is required to plumb the plotted point exactly over 
the station, although on the usual field scale an approximation with the eye is all that is requisite. 
All lines should be drawn lightly and carefully close to the edge of the rule with a finely sharpened 
hard pencil ; but in sketching one somewhat softer may be used. If the table and alidade be in 
proper condition, the contact of the fiducial edge with the paper will be perfect throughout its 
whole length ; and in drawing a Hue along the edge care must be taken to preserve the same incli- 
nation of the pencil, and to avoid a "shoulder" in the pencil itself. If the rule be at all raised 
from the paper at any part, still greater care is to be observed lest the point of the pencil should 
run under the edge and thus deviate from a straight line. 

It would be well for the beginner to learn to use his left eye as well as the right in sighting 
with the alidade, for obvious reasons. 

The instruments should be kept scrupulously clean and free from sand or grit, and work with 
the table should cease the moment the presence of any foreign substance between the surfaces 
which play upon each other is suspected. An occasional taking apart of the table and cleaning 
with soap and water, using soft linen rags for the pupose, will be found necessary; and after being 
oiled and put together, it should be wiped thoroughly dry. The cleaning should not be intrusted 
to any person unaccustomed to the handling of instruments. 

In observing upon signals which are not perpendicular, the sighting should be as nearly as 
possible upon the base of the pole. 

Field practice. — Topographical points can be determined by three methods, viz : "intersection,"* 
"resection," and measured distances. In the first of these the point must be seen from two or 
more occupied points in suitable positions with regard to the point to be determined; in the 
second it must be occupied; and in the third there must be a direct measured line, with an estab- 
lished direction from the occupied point. These methods of determination, and the incidental 
operations which accompany them, will now be considered. 



Custom has given to this general term a specific signification in Coast Survey topographical work. 



AND ITS USE IN TOPOGKAPHICAL SURVEYING. 
Fig. 1. 



13 




4 



Let O, P, Q, B, Fig. 1, represent the board of the plane-table, upon which is spread the topo- 
graphical sheet; the plotted triangulation point a upon the sheet representing the signal A upon 
the ground; &, the spire B; c, the signal C; and s, the station S; the small letters on the sheet rep- 
resenting the centers of the signals on the ground, which are referred to by corresponding large 
letters. 

The table is first placed approximately level over the occupied station S, and put in position, 
also approximately, by the eye, so that the plotted points on the sheet are in range with the station 
S and the signals or objects they represent in the field. Then plunib the point s over the station 
S, fixing the legs of the table firmly in the ground; place the. alidade upon the table so that the 
rule shall extend across its center; loosen the large milled head screw projecting below the top of 
the stand, and by means of the leveling screws bring the bubble of the circular level on the rule 
to the center. Place the alidade at right angles to its first position upon the board, repeat the 
operation, clamp the large screw again, and the table is level. Now free the tangent screw by 
loosening its clamp, place the edge of the rule r upon the occupied point s and the point b, the 
telescope being directed toward the spire B, as shown by the arrow-head in the figure, and revolve 
the table horizontally about its center with the hands until B is seen in the field of the telescope ; 
clamp the tangent screw and turn it till the intersection of the cross-hairs bisect the top or center 
of the spire B. The table is now "in position" if the plotted points be correct and the proper 
objects sighted. In other words, the table is "oriented" when the point observed upon and the 
point occupied are in the line of sight, the edge of the rule being upon the two plotted points; the 
one, s, perpendicularly over the occupied station, and the other, b, the station observed upon. As 
a test of the correctness of this, place the rule upon the point s again, and upon the points a and c 
consecutively, and if the two signals A and are covered by the vertical cross-hair of the tele- 
scope, the orientation is assured, and the meridian of the sheet is parallel to that of the earth, all 
the lines joining the signals and their respective projections being also parallel. 



14 TEEATISE ON THE PLANE-TABLE, 

It will sometimes happen that the upper metal disk attached to the table, after it has been 
clamped and the tangent screw used to put the table in position, has a tendency to spring still 
further with a sudden movement or slight jerk, and this movement may not occur until impelled 
by the ordinary working about the table, and pass unobserved by the operator. This may arise 
from the two disks being screwed too closely together, and the faces in contact not being suffi- 
ciently oiled. It is often the source of much trouble to the beginner, and he is unable to discover 
the cause. It is well, therefore, in orienting the table, when this is suspected, to take hold of the 
edge of the board with the thumb and finger and spring it very slightly from side to side, in order 
that the table may settle itself in a fixed position. The cause of the trouble must, of course, be 
removed on the first opportunity. 

The next operation is to "take the forward line" to the next point which it is desirable to 
occupy or determine, either some natural object which can be occupied, or a forward signal placed 
for that purpose, say the signal D. 

The edge of the rule is placed upon the point s and moved about that point as a center until 
the forward signal D is covered by the vertical hair, and then a line,/, is drawn along the edge of the 
rule from s sufficiently far to reach the estimated distance on the sheet of the point d, and at each 
end of the rule the short check lines n n are drawn. In the same manner lines to be afterward 
intersected should be drawn to such objects as it may be well to determine. To prevent confusion, 
the ends of such lines are marked as in the diagram: ch., chimney; t, tree; cup., cupola; sp., spire; 
w. m., wind-mill, &c. Tangent lines, and lines radiating to objects comparatively near at hand, to 
be chained or obtained by the telemeter, as fence corners, &c, should be likewise taken. If the 
station occupied be in an elevated and prominent position, its height should be observed, both as a 
guide for putting in the contours at the point and to serve as a point of reference in taking heights 
at other places, the method of doing which will be given hereafter. The necessary sketching is 
now done, omitting nothing that can be completed from this point; the alidade removed, the table 
raised, the signal put np, and the party leaves for the next station. Sometimes it is necessary to 
start the chain from the station to the forward signal. 

When moving from one station to another, it is the custom with some topographers to loosen 
the tangent clamp, with the idea that if the table come in contact with any object while being 
transported it will revolve and be less liable to injury. This is perhaps true, if the blow comes on 
the side of the table in the direction of its plane. 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 
Fig. 2. 



15 




\chimiiey- 



^D 



Now let the letters in Fig. 2 be the same as in Fig. 1. The table is removed to the station A 
and placed over the point on the ground, put in approximate position, leveled, clamped, and 
loosened at the tangent screw, as at station S. The rule is then placed upon the line as, the cross- 
hairs of the telescope directed toward the signal S, and the table brought into position, as before 
described. Then, keeping the edge of the rule upon a, direct the telescope upon the signal T>, and 
draw the line ad, intersecting /, and determining the position of the point d upon the sheet, cor- 
responding to D, and bearing the same relation in position and distance to the points s, a, b, and c, 
as the signal D does to S, A, B, and 0. All the other objects to which lines were drawn from s, 
and which can be seen from A, are intersected and determined in the same manner. This is an 
example of the method of "intersection." 

The necessary sketching, determination of height, &c, are executed here as at S, and, indeed, 
at every point occupied, it being desirable, if possible, never to occupy a station more than once. 

The intersection of two lines is not, however, positive evidence of the correct determination of 
a point. Let us, therefore, proceed to D and again determine it by "resection" from the point B. 
(See Fig. 3.) 



16 



k 



TEEATISE ON THE PLANE-TABLE 
Fig. 3. 

L 



\ 



.&- 




The table is placed over tlie point D, put in approximate position, leveled, &c., as at the other 
stations. The rule is then placed upon the forward line, /, (now called the "back line," as seen 
from D,) passing through the point s, so that the checks n n are just visible along the edge, and the 
telescope directed toward the signal S, as shown by the arrow, and the table oriented. The rule 
is then placed with its edge bisecting one of the plotted points, such as 6, which will give a cleanly- 
cut angle (the nearer 90° the better) with the line/, and is moved about that point as a center until 
the spire B is covered with the vertical hair. A line is now drawn along the edge of the rule, 
crossing the line /. If this line intersects/ at precisely the same point as the lines/, a, and d, the 
position of d upon the map is assured, and a delicate hole with the dividers should be pricked upon 
the sheet to fix the point, surrounded by a small circle in pencil. The point may be still further 
tested by resection from C. If the forward line from s has also been chained, the distance 
taken from the scale and laid off from s on the line /will afford still another test, and it is quite 
sufficient if it agree with an intersection where only one can be obtained. 

Another forward line, /', is now taken, with the usual checks, %' n f , to the next desirable sta- 
tion, and lines of intersection are also drawn from d upon the chimney, wind-mill, cupola, tree, and 
spire previously observed, as they appear in the telescope, in succession from left to right, and their 
positions definitely fixed upon the map, pricked through and marked ; and these being well deter- 
mined, can now be used for the determination of other stations. ~New lines to such other objects 
as may be thought necessary should be taken, as well as tangent lines, and then follows the sketch- 
ing to fill in the details about the station. 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 
Fie\ 4. 



17 




The table is now removed to E, Fig. 4, (which it was thought unnecessary to mark on Fig. 3,) 
through which the forward line from d is supposed to pass, and is placed over the station ; and the 
point e, representing the projection of the signal E upon the map, is determined by resections by the 
use of the line/' and the points s, a, b, and c, although the latter two are not absolutely necessary. 
The spire and tree may also be used for this purpose. Those points which, owing to acute inter- 
sections, have been insufficiently determined, as the chimney, cupola, and wind-mill, are again 
intersected. Other intersecting lines are taken from e upon other points which present themselves, 
the necessary sketching made, and a new forward line taken to the next station. 

During all these operations occasional recurrence should be had with the alidade to some 
established point to assure the immobility of the table, or to correct any deflection from the true 
position which may have taken place. 

If upon going to a forward signal or object to which a line has been taken it is found that it 
cannot be occupied, or that it is in such a position that a sufficient number of points cannot be seen 
from it, or, for any reason, it does not answer the desired purpose, a poiut in range between the 
two stations, or upon the prolongation of the line connecting them, can be occupied. Getting into 
line between the two stations is performed by two persons standing facing each other, about thirty 
meters apart, and as nearly on the line as possible, one of whom sees the back and the other the 
forward signal. Each then moves alternately to the right or left, as directed by the other, until 
each signal is in line with the person whose back is toward it, as seen by the person facing it. 
The table can then be readily placed anywhere on the line. A position for a point beyond the 
forward signal may also be found by simple alignment with the two signals. 

When by accident in drawing a forward line from an occupied point, near which upon the 
sheet is plotted another or several other points, the rule is not set upon the point occupied, and the 
error is not manifest until the forward signal is reached, instead of going back to take the line over 
and draw it from the last station, it can be constructed by drawing from the correct station a par- 
allel to the false line. 

Points and lines. — The accuracy of the work on the topographical sheet is primarily and mainly 
dependent Upon the correct determination of points, and a want of an exact knowledge of the capa- 
bilities of known points to determine the observer's position anywhere upon the sheet, as well as 
the positions of the other points, is one of the greatest sources of trouble and error to a beginner. 
When a survey is commenced with slightly faulty points, and uncompensated as the work proceeds, 
the scale upon which it is executed becomes variable, and consequently erroneous. 

When, as we have seen, a triangulation poiut is occupied, and lines drawn from a number of 
A 22 3 



18 TREATISE ON THE PLANE-TABLE, 

other plotted points with the table in position intersect perfectly at that point, the position is 
assured; but when they do not thus intersect, the cause of the difficulty may be found either, 1st, 
in errors of triangulation or computation; 2d, in a faulty projection or plotting of the points; or, 
3d, in the unequal expansion or contraction of the paper. The first two, when at all great, can 
only be corrected by a revision of the work of triangulation and projection ; and the latter, if not 
sufficiently large to warrant an entire rejection of the sheet, can be remedied only by the judicious 
ction of the topographer, with the plane-table, in the field. 

When the points disagree within quite moderate limits, an experienced topographer can, by 
distributing the error among the points in the proportion of their distances from the occupied point, 
so reduce the effect of the sum of these distributed errors on the position of the occupied point that 
he may be safe in considering positions determined from his point, so corrected, as more accurate 
and trustworthy than the plotted points themselves, and use them as such. A maximum error of 
twenty meters on a scale of yotjo o can generally be reduced at the point of intersection to an almost, 
if not quite, imperceptible quantity. 

The topographer should be slow to reject a point as unfit for use. No matter what the apparent 
disagreement may be, one set of points should not be hastily thrown aside and another accepted because 
one set appears to agree and the other to disagree. But the positive occupation of a series of points 
whose accuracy thus becomes established, and of another series whose inaccuracy is equally well 
determined, renders the preference of one set over the other at times not only permissible but obliga- 
tory. It should always be remembered that absolute and careful investigation in the field, and close 
examination of the projection, plotting, and data of triangulation ought to be made before any 
point or set of points is condemned. 

THREE-POINT PROBLEM. 

It is often expedient to set up the table in position at an undetermined point without any back 
line on which to set. With three signals in view whose positions are projected on the map, the 
table can be oriented and the point determined by means of the " three-point problem." 

The table is brought into approximate position by the eye or declinatoire, and, not being 
properly oriented, the lines drawn from the three projected points will not intersect in one point, 
except when all four are on the circumference of a circle. In this case the " two-point problem" 
is available. Except in this instance, however, the lines will form a small triangle, called the tri- 
angle of error, or two of them will be parallel, intersected by the third. The position of the true 
point can then be determined geometrically from these several intersections, and is always at the 
point of intersection of arcs of circles drawn through each two points and the point of intersection 
of the lines drawn from them ; but the construction of these arcs is inconvenient in the field. More 
practicable modes of locating the points sought will be given in their order. 

In the classification given below, based upon the location of the true point in relation to the 
triangle of error, the triangle formed by the three fixed points is called the great triangle, and the 
circle passing through the same points the great circle. 

Class 1. — When the point sought falls within the great triangle, the true point is within the 
triangle of error. (Case 1.) 

Class 2. — When the point sought falls within either of the three segments of the great circle 
formed by the sides of the great triangle as chords, (Case 2,) or without the great circle and within 
the sector of the opposite angle of either angle of the great triangle, (Case 5,) the true point is on 
the side of the line from the middle point opposite to the intersection of the lines from the other 
two points. This also includes Case 3, where the three fixed points are in a straight line, in which 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 19 

oase the points are considered as being in the circumference of a circle of infinite diameter, and the 
t^ue point always lying in one of the segments of the great circle. 

Class 3. — When the point sought falls without the great circle and within the sector of either 
angle of the great triangle, the true point is on the same side of the line from the middle point as 
the intersection of the lines from the other two points. (Oase 4.) 

In case the point sought falls on the range of any two of the points, and the table is deflected 
from true position, the lines from the two points will be parallel, intersected by the line from the 
third point. But this range can always be determined by alignment, the table set in position on 
the range, and the point occupied determined by resection on the third point. (Case 6.) 

In case the point sought falls near the range of any two of the three points, the lines from the 
two poi its are so nearly parallel that their intersection falls off the table, but the relation of the 
true po 1 nt to the triangle of error is in no way changed. 

T e accompanying diagram shows the fields embraced by the classes given above, also the 
location of each of the cases included in those classes. 

A point on the circumference of the great circle being indeterminate, it is apparent that a 
determination should not be attempted in close proximity thereto, if better conditioned points are 
available. 

The following cases are believed to include all possible conditions of the relation of the posi- 
tion of an undetermined point to three fixed points. The surveyor is supposed to face his signals 
and the directions right and left given accordingly : 

Case 1. (Figure 1, Plate 31.) — When the point sought is within the great triangle, the true 
point is within the triangle of error. 

a b c are the projected points, and ab ac be, the false intersections from them forming the tri- 
angle of error. 

Bide. — If the line from any one of the points falls to the right of the intersection of the other 
two, turn the table to the left, and if to the left, turn it to the right. 

When the point sought is without the great triangle the true point is also without the triangle 
of error, and is situated to the right or left of it, according as the table is out of position to the left 
or right. 

Case 2. (Figure 2, Plate 31.) — When the point sought is without the great triangle and within 
the great circle, the true point is without the triangle of error, and the line drawn from the middle 
point lies between the true point and the intersection of the other two lines. This also includes 
Case 3, (Figure 3, Plate 31,) which rarely occurs in practice, where the three points are in a straight 
line. 

Rule. — If the line from the middle point is to the right of the intersection of the other two, 
turn the table to the right, and if to the left, turn it to the left. 

Case 4. (Figure 4, Plate 31.) — When the point sought is without the great circle, and the 
middle point is on the far side of the line joining the other two points, the true point is without 
the triangle of error, and upon the same side of the line from the middle point as the intersection 
of the other two lines. 

Rule. — If the line from the middle point is to the right of the intersection of the other two, 
turn the table to the left, and if to the left, turn it to the right. 

Case 5. (Figure 5, Plate 31.) — When the point sought is without the great circle, and the 
middle point is on the near side of the line joining the other two points, the true point is without 
the triangle of error, and the line drawn from the middle point lies between the true point and the 
intersection of the other two lines. 



20 TREATISE ON THE PLANE-TABLE, 

Rule. — If the line from the middle point is to the right of the intersection of the other twr» ? 
turn the table to the right, and if to the left, turn it to the left. 

Case 6. (Figure 6, Plate 31.) — When the point sought is on the range of either two points, ajad 
the table deflected from true position, the lines drawn from these points will not intersect, but, will 
be parallel, intersected by the line drawn from the third point ; the true point is then between the 
two parallel lines. 

Rule. — When the line from the right-hand station is uppermost, turn the table to the right, 
and when that from the left hand is uppermost, turn it to the left. 

Practicable modes of determining the position of a fourth point by resection upon three fixed points. 

1st. Lehmann , s method. (Figure 7, Plate 31.) — This method is based upon the fact that the point 
sought is always distant from the three lines drawn from the three fixed points in proportioa to the 
distances of the latter from the point occupied. 

ABC are the projections of the three signals from which it is desired to determine by resec- 
tion the position of a fourth point D. The table being out of position to the right, the triangle of 
error formed by the three lines from A B and C is ab ac be. The true point occupied lies at D, 
being at the intersection of the circles AB ab, AC ac, BO be. Now, if perpendiculars be drawn 
from D to the lines drawn from A B and 0, we shall have 

Da : T>b : : DA : DB, or T>b : Be : : DB : DC. 

The relative distances of the point occupied from the three signals must be estimated and the 
point located in reference to the three lines from A B and C accordingly. 

Nettd's method. (Figures 8, 9, and 10, Plate 31.) — This method of determining the true position 
from the false intersections is ingenious and of much practical value. 

The table not being properly oriented, and having resected upon a b and c, we have the triangle 
of error ee'e". Now, by the Lehmann method, judge of the position d, (the point sought.) Set the 
alidade on db and revolve the table so that the line of sight passes the signal B. Besect again on 
a b and c, and we have the triangle of error gg'g". Join e and g, and through both points draw 
parallel lines ii and kh. Lay off ei=ef and gk=gh. Join i and ft, and the intersection I lies in 
the line of sight from the true point to the middle point b. Set on this line, resect upon a and c, 
and d is the point sought. 

If the two triangles of error are situated on the same side of the true line of sight to the middle 
point, the parallel lines are set off on one side of eg only. 

The triangles of error ee'e" and gg'g" are always similar, Zg"=Ze', Zg'=Ze", Zg=Ze, and 
as the two points e and g are always in the circumference of the same circle, if the table is deflected 
equally on the opposite sides of the true line of sight to the middle point, the triangles of error will 
be equal and ef=gh. On the true line of sight gh and ef=0. 

In the triangles gkl and eil, ii and M being parallel, Zg=Ze, Zl is common, therefore Zlc=Zi, 
and the triangles are similar, and el : gl::ei(=ef) : glc(=gh). 

(Figure 9, Plate 31.) — The point sought (d) must lie in the circle passing through aec, and also 
through age. Draw the circle agdecs, join s with e and g, then we have 

Zdse= Zdce and Zdsg=Zdag 

Zdce= Zdbe" and Zdag=Zdbg" 

Therefore Zdse=Zdbe" and Zdsg=Zdbg" 

also se parallel to be" and sg parallel to bg" 

and the triangles sle and blf are similar, 

and the triangles slg and blh are similar; 



A.ND ITS USE IN TOPOGKAPHICAL SUKVEYING. 21 

from which we get le : If:: Is : lb 

and lg : Hi ::ls : lb, 

also le : If: : ?</ : Ih and fe : te — If: : lg : lg — lh 

that is el : efy.gl : gh, ov el : gly.ef : gh. 

The amount of the angle at I is always an indication of the value of the determination of the 

nt sought. The more obtuse the angle the better the determination. 

bessel's methods. 

Bessel gives two methods, both based on the same principle. 

First method. — (Figures 11, 12, and 13, Plate 31.) 

Let a b and c be the projections of the three points observed upon, and ab be ac, the triangle of 

error formed by resection upon them when the table is not in position. Lay off be' on ba=bc, 

xtend be and lay off ba'=ba. Call the angle at the intersection ab=x, and that at the intersection 

bc=y. At a' lay off toward you Aba' e=Zy, and at c' in the same direction /.be' e=Zx. The lines 

o laid off will intersect in e, which lies in the line of sight through the middle point b and the point 

sought, (d.) By resection upon a and c, the position of the point on this line is fixed. 

The solution of this is as follows, (Figure 14, Plate 31) : Lay off at a the angle bae=Zbdc, and 
at c /bce=Zbda, drawing the line be, Zebc— Zabd and Zeba= Zcbd. Produce be to/, so that bf=ba, 
and draw/<y parallel to ce. Lay bfg on ba, so that /falls on a and g on li. 

Then we have in the quadrilaterals ahbe and abed 

Zbae=Zbdc, Zhbe=Zabc 

hb : be::bg : bey.bf : bcy.ba : be. 

The two quadrilaterals are therefore similar, and hence 

Zebc= Zhba= Zabd 
and Zeba=Zebd. 

Second method. — The plane-table may also be put in position without the use of the points a' 
and c'. (Figures 15, 16, and 17, Plate 31.) 

On ac at c lay off Zace=Zx, and at a lay off Zcae=Zy. The lines so laid off will intersect in e, 
which lies in the true line of sight through the middle point b and the point sought, (d.) Resection 
upon a and c then fixes the position of d. 

The angles e and d of the quadrilateral aecd are equal by construction to two right angles ; 
hence a circle may be described about the quadrilateral, and we have the periphery angles 

ace=adb 
and cae=cdb. 

This latter method, being simpler, is better than the first, but, under certain circumstances, one 
may be used when the other cannot. If, for instance, by the last-mentioned manner of construc- 
tion, the point of intersection (e) should fall outside the plane-table, it may possibly be made to fall 
inside by the first method. Again, if, by the latter method, the angles of intersections happen 
to be right angles, or nearly so, then the two plotted lines to e become parallel to each other, or 
nearly so, in which case the first method may be used with advantage. 

The best mode of constructing the angles x and y upon ac is with the alidade ; directing the 
line to one of the objects and observing the other object with the alidade set upon the point at 
which the angle is to be set off. It can also be readily done with the dividers by laying off the 
chord of the angle. 



22 

Should either or both of the angles set off at a and c be so obtuse that the point e falls off the 
table, a shorter base can be used, drawn parallel to ac, as near to b as may be necessary. 

TWO-POINT PROBLEM. 

The occasion may arise where it is desirable to place the table in position at a given point, 
from which point only two deter mined points are visible. This may be done by the following methods. 
The first mode possesses the virtue of making no linear measurement, and demonstrates in a very 
satisfactory manner the power of the table in determining position by resection. (Figures 18, 19, 
20, and 21, Plate 31.) 

Two points, A B, not conveniently accessible, being given by their projections a b, to put the 
plane-table in position at a third point C. (The capital letters refer to points on the ground and 
the small ones to their corresponding projections.) 

Select a fourth point D, such that the intersections from G and D upon A and B make suffi- 
ciently large angles for good determinations. Put the table approximately in position at D, by 
estimation or by compass, and draw the lines Aa Bft, intersecting bid; through d draw a line 
directed to C. Then set up at 0, and assuming the point c on the line d 0, at an estimated dis- 
tance from d, and putting the table in a position parallel to that which is occupied at D, by means 
of the hue cd, draw the lines from c to A and from c to B. These will intersect the lines d A, d B 
a t points a' and b', which form with c and d a quadrilateral similar to the true one, but erroneous 
in size and position. 

The angle which the lines ab and a'b' make with each other is the error in position- By con- 
structing now through c a line cd' making the same angle with cd as that which ab makes with 
a'b'. and directing this line cd' to D, the table will be brought into position, and the true point c 
can be found by the intersections of aA and bR. 

Instead of transferring the angle of error by construction, we may conveniently proceed as 
follows, observing that the angle which the line a'b' makes with ab is the error in the position of 
the table. As the table now stands a'b' is parallel with A B, but we want to turn it so that ab shall 
be parallel to the same. If we, therefore, place the alidade on a'b' and set up a mark in that direc- 
tion, then place the alidade on ab and turn the table until it again points to the mark, then ab will 
be parallel to A B, and the table is in position. 

Another method is as follows : (Figure 22, Plate 31.) 

Two points, A and B,not conveniently accessible, being given, to put the plane-table in position 
at a third (undetermined) point, 0. 

Set up the table at the point sought as nearly in position as can be done with the eye, and 
resect upon A and B, intersecting the line be at c'. The angle ac'b is the true angle at the point 
occupied, subtended by A B, being the angle of nature actually drawn ; therefore, the true point 
must be on the circumference of the circle passing through abc'. Construct this circle. Measure off 
a base, C D, at least half the length ol C B, at right angles, or nearly so, to be, in either direction 
most convenient. Set up a signal at D, and with the alidade draw the line c'd. Eemove the table 
to D, and, by means of a signal at 0, (the point sought,) and the line dc', bring the table into a 
position parallel to that which is occupied at C. With the alidade centering on d, observe the signal 
B, and draw the line db' intersecting cb at b'. c'b' is the distance of the point C from B, and this 
distance laid off on the circle ac'b as a chord from b will give c", the true position of the point 0. 
A fourth point may then be occupied, and by resection upon A B and C the accuracy of the deter- 
mination of verified. 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 23 

Where it is possible to get the two signals A and B in range, it is easy to determine the 
position of a third point by a mode long practiced by topographers. 

Set np the table anywhere on the range line, and, having set up a signal at the point sought, 
resect upon it, intersecting the range line anywhere, and, by means of the range signal and the line 
to it, the table may be set in parallel position to that occupied in the range, which is the true 
position, and the point sought may be determined by resection upon the two fixed points and their 
projections. 

FIELD-WORK. 

In taking lines of intersection upon a point or object from a series of stations, when these lines 
do not coincide in one point, as they are usually derived from stations at unequal distances from 
the point, the error should not be divided equally among them, but in proportion to their lengths. 

It should be borne in mind that very short lines from a determined point — as, for instance, 
to the corners of a fenced road, where the table occupied the center of the intersection of two 
roads — may be taken with no apparent error when the table is deflected to some extent from its 
true azimuth, but that in this case a prolonged line will be considerably out at its further extremity. 

A long line should never be obtained by the prolongation of a short one from a back station 
where there is no small check line, or some other point in that prolongation already fixed. 

It will be apparent that the more nearly at right angles intersecting lines cross each other, 
the more clearly the point will be defined ; acute intersections, as far as possible, should be avoided, 
and, even when they are crossed by a third line at a satisfactory angle, a fourth line, or an accu- 
rately chained distance from a well-determined point, is advisable. 

The necessity for dependence upon a measured line, with an established direction alone, for 
position is sometimes unavoidable; but, except for minor details, it should never be resorted to 
when other means are available, and, in finished work, no lengthened consecutive series of chained 
lines for positions should be trusted without resections for tests of accuracy. It is safer to combine 
both, unless the supply of signals is ample and they are favorably located. 

A judicious use of range lines from established points, or signals, will much economize time 
and facilitate work. 

Two range lines from well-determined points are equivalent in value to four intersecting lines. 

Tangent lines can only be used for determining the edges of woods, bends of streams, sweeps 
of shore-line, outlines of shoals, small ponds, and the outlines of other objects when in unimportant 
localities, and are inadmissible for any purpose in which accuracy of delineation is required, save 
when they form a polygon, by which absolute convexity at all points is to be represented, and even 
then the points or objects should be visited and sketched, if possible. 

Where the topography surveyed includes the shore-line of a body of water, and immediately 
precedes the hydrographic survey thereof, as in the Coast Survey, it is the duty of the topographer 
to locate and determine the shore signals, and they should be placed so as to furnish the hydro- 
graphic party with the best points available for the determination of positions on the water. 

It is well to mark all stations occupied along or near the shore by pegs driven into the ground 
with stones about them, so that their positions may be found by the hydrographer if the signals 
should be destroyed, and he can then select such as are best adapted to his use. 

Natural or artificial objects along the shore, or in plain sight from the water, such as fence 
ends, rocks, prominent houses, and posts on wharves, &c, should be determined and marked upon 
the sheet. As some time may elapse between the labors of the two parties, the stations should be 
well secured above the wash of the tides. 



24 TEEATISE ON THE PLANE-TABLE, 

Lines to buoys and other permanent floating objects should be, as far as practicable, taken at 
the same stage of the tide, or direction of current, or the status of the tide noted at the time of 
observation. 

In the determination and tracing upon the chart of the low- water line, so much in its outline 
is generally dependent upon the direction and force of the wind that no fixed rules for guidance 
can be given. 

The delineation of the ordinary mean low-water mark should be aimed at, and when it is 
beyond the reach of the plane-table, and presents no marked points for determination, or is of a 
character that will not admit of putting up and working the instrument — as along swampy shores 
of the South, where the muddy shoals extend far sea-ward, and among the shifting quicksands of 
our great estuaries and bays — it must be left to be traced by the soundings and tidal reductions of 
the hydrographic parties. 

It is always best to determine the high and low water lines, both at spring and neap tides- 
Having learned the range of tide, the topographer will know how long he can work without error. 

Where, on the occurrence of any great or unusual storm or freshet during the working season, 
the low- water line, which has already been surveyed, is found to have changed in form or locality, 
it should be resurveyed, and both the old and new outlines retained on the sheet, with the appro- 
priate notes. 

As a feature which is quite interesting and important under certain circumstances to the 
hydrographer, low-water springs, having their origin and outlet below the high-water line, should 
be shown on the chart, where it can be done, in the regular routine of work. All grassy shoals 
should be delineated. They are always found in water scarcely agitated by waves or currents, and 
their shape and outline on the channel side is a very marked feature, and a good measure of the 
power of the current. Eel grasses should also be put upon the map, as indicating an antecedent 
accumulation of fine sand or soil. 

Orientation by the declinatoire or compass-needle, alone, is not reliable, unless for obtaining 
positions for rough sketching in plane-table reconnoissance, but it may be useful as an adjunct 
when an operator, in default of sufficient points, desires to obtain an approximate position. It is 
used by placing the straight edge of the box containing the needle upon a magnetic meridian, 
previously traced upon the chart, and revolving the table until the needle points to 0°, or north, 
on the graduated arc in the end of the box. The magnetic meridian is roughly obtained at any 
well- determined station, when the table is properly oriented by the use of the declinatoire itself 
the meridian line being drawn upon the sheet along the straight edge of the box when the needle 
points to 0°. When the declinatoire is fastened to the rule of the alidade, the line is drawn along 
the edge of the rule. 

In sketching or drawing, care should be taken not to lessen the size of natural objects, the 
scale being followed as far as practicable ; but in some cases, which will be apparent, it may be 
desirable to enlarge somewhat, but very cautiously. The topographer shoidd learn to draw from 
nature readily, and at once, without being obliged to erase or interlineate. 

By working carefully at first, facility in this will be arrived at in due time. 

Too frequent use of India-rubber disturbs the fibers of the paper and renders the subsequent 
inking less neat and clear. The drawing should be plain and distinct, so as not to be obliterated 
easily by the movement of the alidade over the paper, but not so dark or heavy as to blur. The 
object should be solely to represent accurately the surface and elevation of the country surveyed, 
and it should be easy and natural, and not a stiff copy of conventional signs. 

As far as practicable all work should be drawn in the field under the eye. Sketching and 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 25 

plotting iii the office from notes is objectionable, unless the country be near at hand for examina- 
tion in case of doubt or a defective sketch or of error of chaining. 

Too great care cannot be taken in the manipulation of the plane-table. There should be no 
pressure, and in moving the alidade both it and the arm should always be raised clear of the board, 
so as not to rub over the surface of the sheet. 

The topographer should learn to distinguish, as a matter of economy in point of time, between 
the relative importance of different topographical features. While it should be the object to do all 
the work correctly, yet a discrimination should be made between the expenditure of time necessary 
to a correct representation of the thickly-settled streets of a town and the bend of a small creek in 
an obscure and unimportant swamp. 

CONTOURS. 

If there be any feature which more peculiarly distinguishes one section of a country from 
another, imparting to it its most striking characteristic, and to which all other accidents of ground 
are subordinate, it is to be found in the inequalities or changes of the elevation of the surface, and 
it is the correct representation of this feature that calls forth the best skill and judgment of the 
topographer, and upon which the value of a map most materially depends. 

Previous to the commencement of work, it is well to become possessed of some knowledge 
of the country which is to be surveyed. A rapid examination of the ground, by showing whether 
it lies in regular parallel ridges and intervening valleys, isolated hills, gradually sloping plains, or 
broken, abrupt, and rocky declivities, and whether partially or entirely open or wooded, will sug- 
gest to the topographer the best method of operation, and enable him to form a general plan of 
work which will result in economy in point of time, and as a consequence will preserve the con- 
tinuity of contour frOm day to day as the work progresses. 

By keeping in view the characteristic features of the hills in the section of country under 
survey, the topographer will be able to give a naturalness to a sheet, which by a mere formal 
delineation by prescribed rules he could not obtain. It is to be observed that the elevations and 
depressions, in their form and course, follow, or rather are a part of, a general system of nature, 
however capriciously detached localities, or even extended areas, may appear to be excepted from 
the general law. Where these exceptions are found they can usually be traced to some breach of 
or interference with this law, and will be found to be confined solely to the locality where the dis- 
turbing causes operated. 

Thus the principal ridges will be found to tend in one general direction, either running par- 
allel with a main range which lies further off, or forming spurs at right angles to it. Along the 
coast the latter is generally the case, as we there usually find the spurs, or the extremity of some 
maiu prominent inland range. When a single detached hill is found, or a series of them, present- 
ing, as is sometimes the case, so smooth and regular an outline as to be compared to half a water- 
melon, and apparently located without any reference either in direction or character to the other 
elevations of the vicinity; and so also when the ground presents the appearance of a confused 
mass of broken bluffs, rocky faces, and cleft surfaces thrown together without any apparent regard 
to order or regularity, it will be found that the general delineation, when followed far enough, will 
show that the contours, whatever may be their local complexity and irregularity of outline, follow 
the same general direction as the main ridges of the sheet. Along the intermediate shores, upon 
islands, or long arms running far out into the sea, where the sandy knolls, or dunes, and ridges, 
shift or change their outline under the influence of wind and tide, an exception is found which calls 
for careful delineation, and the peculiar and striking character aud forms of these should be por- 
A 22 4 



26 TREATISE ON THE PLANE-TABLE 



trayed with all possible exactness as an interesting and useful aid in the study of a correlative 
branch of geodesy. 

To the meteorologist and to the physical geographer the careful mapping of dimes is valuable; 
for however familiar the locality may be, no eye-view can discover those recurring features which 
are found in the map of an extended district. 

If a sandy district is exposed to permanent or prevalent dry winds, traveling dunes will be 
found. These are distinguished from other hills by the contrast between the fore slope, (on the lee 
side,) which is steep, -and the near slope, (on the windward side,) which is gentle. Successive sur- 
veys on sandy coasts, where close attention has been given to the contours of the dunes, are of 
great value for comparison if every detail is carefully given. Even in places where the winds are 
uncertain, proper contouring discovers dunes which travel along the resultant of the forces, and in 
the direction of this resultant the great dip of the fore slope is found. For such dunes the several 
slopes for different points of the compass are equally interesting. 

On exposed points projecting far into the sea, peculiar dunes, called galls, are found. They are 
long ridges of sand, broken by slough-ways. It has been observed that sometimes these slough- 
ways are parallel. Correct and well-contoured topographical maps of the localities where they are 
found would aid much in a study of this interesting subject. Contours only would discover their 
order and exhibit the material system, which could not be done by a representation by hachures. 
The delineation of bluffs along the -shore should also, for like reasons, be carefully executed, 
nnd when it is possible a representation of their slopes should be given. Bluffs, if worn by the 
waves, will usually exhibit three slopes: 1st, the caving slope at the top; 2d, the talus; 3d,, the 
apron or flat, exposed wholly only at very low tides. The caving slope is sometimes perdendicular 
where tertiary country is being worn away — never where old dunes are yielding. The talus is 
usually of selected material — stones, perhaps. The talus and flat are generally wanting in bluffs 
worn by currents. 

As has been said, in no branch of surveying does so much depend upon skill, combined with 
good judgment and experience, as the faithful representation of hills over an extended and diver- 
sified area, and long practice and close observation only can give facility and accuracy in its 
execution. 

Various methods, more or less defective in presenting a correct idea of elevations and depres- 
sions, have. been contrived for topographical surveys; but the graphic representation of the succes- 
sive gradation^ of level by means of horizontal lines, as at present employed in the Coast Survey, 
gives the nearest approximation to nature which has yet been devised, and when faithfully executed 
must necessarily express very nearly, if not exactly, the shape and height desired. 

Contours, or horizontal curves, are the outlines of horizontal sections of ground at different 
elevations, with designated equal intervals between their planes, delineated in their true positions 
relatively to each other and the rest of the map, and agreeably to the scale of the map itself; or, 
briefly, a contour is the curve produced by the intersection of a horizontal plane with the surface 
of the ground. 

Perhaps contours may be described more simply as imaginary shore lines formed at stated or 
regular elevations by the water which is supposed to rise successively to these elevations over the 
face of the country. 

As each curve has equal vertical ordinates at all points, the elevation or profile of a hill, as 
well as a model in relief, can be constructed directly from the map, when it is accurately executed 
on a large scale, without further field measurements. 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 27 

A profile of a lull is the outline or trace formed with its surface by a vertical plaue cutting 
the hill in any direction. 

The anuexed diagram, from actual survey, shows the profile, through the line A'B', of the hill 
H, as represented on a topographical map. The full parallel lines upon the profile represent lines 
of equal elevation for every twenty feet difference of level, and the broken or intermediate lines 
xxx, those of ten feet. 

A reference to the letters upon the diagram is all that is necessary for a full understanding of 
the subject; a is the shore line or high-water mark upon the map, x x x are the auxiliary ten-feet 
curves, /' the coincidence of curves upon the chart at the perpendicular face of the hill, / upon the 
section. This is the only case where contours of different heights run into each other upon a topo- 
graphical plan. D' D' are depressions in the face of the hill, represented on the profile byDD; 
d' is a barranca or dry broken gully, and c' c' a water-course. 

It will be plain that if we were to suppose the water to rise to a height of twenty feet above 
the high-water line, or to h on the profile, the twenty -feet curve upon the map would then become 
the shore line, and the depression D' would become a pond of water ; and if the water were to rise 
to a height of thirty feet, the dotted broken line would form the shore line, and the knoll Gr would 
become an island. 

Horizontal curves are drawn upon the map with the eye, after having obtained the elevations 
by means of which their positions are fixed, by the measurements of vertical angles with the arc of 
the alidade, or in detailed or special surveys with the level. Where the slope is regular and toler- 
ably steep, the tracing of them is attended with but little difficulty; but where the rise is very 
gradual, giving large horizontal distances between the contours, even when the vision is unob- 
structed, or where the country is much broken or thrown into irregularly- shaped knolls and 
depressions, presenting an intricate and confused variation of surface, the correct representation 
is, at times, very perplexing. 

As in some instances, owing to the smallness of the angle to be measured, the vertical arc 
cannot be relied upon for close determination of heights, and it is evident that the nearer to a level 
a country is, the nearer it is necessary to obtain the exact elevation for the location of the contours, 
recourse to the leveling instrument is indispensable. With the beginner the observations for eleva- 
vation can hardly be too frequent, and he should constantly bear this in mind while at work, as well 
as the necessity for leaving frequent well-marked points of reference wherever they may be of value 
for determination of subsequent heights. 

When triangulation points are occupied, or positions are determined by the plane-table 
preliminary to the regular work; in fact, whenever any station is occupied, its elevation should be 
determined, as well as the heights of such other prominent points or objects as may be visible from 
it. Then in using these in working by resection, the topographer has as many points of reference 
for the determination of height as he has for determining his position. 

It is well, also, to get observations for heights as often as possible upon or from the plane of 
reference or high -water mark; and advantage should be taken, whenever the opportunity occurs, 
of observing from the shore line in wooded districts upon any hill tops or conspicuous objects 
exposed by openings, and also upon rocks or any other natural or artificial objects upon the sides 
of the surrounding hills. 

Where the heights of certain points have been determined by the triangulation party, or a few 
prominent ones have been determined with special care by the theodolite or level, they should be 
used as often as possible as points of reference. 

When hills are inaccessible, the determination from accessible points of both the positions and 



28 TREATISE ON THE PLANE-TABLE, 

heights of objects upon them, such as trees, rocks, stumps, &c, from which the positious and courses 
of the contours can be determined, should be sought for, and in thick forests the roads, paths, or 
the dry beds of streams may be found available for the use of either the vertical arc or level. 

Under certaiu conditions, as those of densely wooded heights and vales, inaccessible, precip- 
itous ledges and bluffs, &c, the operations of the surveyor are limited to an almost entire depend- 
ence upon the eye alone. This cannot be relied upon as accurate, and should be avoided as much 
as possible. 

It is customary to represent on the usual Coast Survey field sheets of T q }- q scale contours of 
successive heights of twenty feet; but occasionally, owing to marked accidents of ground, it is 
deemed advisable to insert intermediate or auxiliary curves to develop the forms lying between 
them. On a scale of T -^oo, contours for every three or five feet difference of level are frequently given. 

Contours should be filled in from each station while carrying on the regular work, when it is 
possible to ascertain heights for that purpose; and in selecting positions for forward signals, and in 
prosecuting the work, reference should be had to the continuous and successive tracing of the con- 
tours on the map, both of those which are filled in at and those from the station, as this will gener- 
ally prove an economy of time, and the work can be executed with more facility. When the topog- 
rapher is at a station whose elevation has been accurately determined, lines should be drawn to 
objects of equal height in all directions and so marked, subsequent intersections giving their posi- 
tions; this will be found of great assistance in running contours and as checks on heights by verti- 
cal angles. Care should be taken in sighting to distant objects to allow for the curvature of the 
earth. 

"With regard to the method of putting in contours from the base of the hill upward, or vice 
versa, opinions differ, some preferring one course, some another ; but it makes but little difference, 
if the height of the point of beginning be correct. Neither of these systems should be specially 
adopted, but the peculiarities and demands of the other topographical features should be considered, 
and all should be worked together to the best advantage, so as to make the work at each station as 
complete as possible before leaving it. 

When, as often happens, the work has been carried on in a wooded country, in a place where 
observations for height have not been made for a long time, then the importance of coming out upon 
some point of known elevation is evident. 

If this is impossible, as is sometimes the case, as in the filling in of the topography in dense woods? ■ 
in a rolling country, where the topographer is confined to the roads, frequently with very short 
sights, and there is no check to come out upon, or when the work closes on the edge of the sheet, 
the use of the level in the hands of an aid, though consuming time, is indispensable. 

The determination of the heights of artificial features, such as fence corners, houses, &c, as an 
assistance in contouring, should not be neglected. 

When the contour runs very near any remarkable accident of ground, as a prominent spur or 
indentation, on general field maps of T o£ S o scale, a slight deviation above or below its true plane is 
admissible, although it is preferable to represent it by the introduction of the auxiliary curve, as 
shown in the sketch. 

It is very desirable that all features within the twenty feet curves, such as breaks in the ground, 
isolated boulders, rocks, &c, which cannot be legitimately represented by auxiliary curves, should 
be shown by hachures or conventional signs. When the rocks have a distinct stratification, or 
when cleft in certain directions, it should be indicated, if they or the scale of the map be sufficiently 
large to warrant it. 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 



29 



It may happen that small features, which are unimportant in themselves, may interfere with 
the development of the general form of the contours, or their introduction may tend to produce 
confusion ; these are best omitted, but this omission should be optional only with one of experience. 
It is dangerous to give latitude in this respect to a beginner. 

When there is an abrupt rise, as in low bluffs, railroad embankments, &c, not above ten feet 
in height, on a scale of yoJoo? ^ should be indicated by hachures always tapering downward, and 
all hachures should, in their direction, follow the downward flow of water or alluvion. 

Depressions of the ground in the midst of level tracts, or upon tops or slopes of hills, unless 
distinguished by ponds or marsh, should be marked with the letter D in red. 

The distinct summits of hills should be marked in figures when they form characteristic or 
remarkable features of the country. 

In measuring for heights or depressions with the alidade, the plane-table is carefully leveled 
and firmly clamped, the telescope is directed toward the point of observation, and moved until the 
cross-hairs are in the same vertical plane as the observed object. The telescope is then clamped by 
means of the screw at the top of the arms of the vertical arc, and the central cross-hairs, at or near 
their intersection, are brought to cover the observed point by means of the tangent screw attached 
to the graduated arc. The angle read, and the distance between the occupied point and the 
observed point measured on the map, the height is taken from the table, which is appended. 



Example. — Observations for height at an occupied plane-table station. 



• 
Stations observed. 


a 
a 
•a 
> 

o 


Distance in me- 
ters. 


Eelative height in 
feet of plane-ta- 
ble station. 


'> -^ 
o a 

(h — 

9 a 
S-2 
.5fS 

W 


V 

a 

°.9 

,a a> 


■S..S 

S a 
■Sa 

O O 

<u u 
£ M 

6° 


• 


' 

1 57 
02 

2 13 


1,756 

940 
539 


+197. 4 
— 2.0 

+ 68.7 


0.0 
201.3 
126.9 


4 
4 
4 


193.4 




195.3 




191.6 








193.4 







Detail of use of table of heights. 

Shore signal : 

1° 50' for 1,700 meters = 179. 00 feet, 

1° 50' for 50 meters = 0. 1 of 500 meters = 5. 26 feet. 

1° 50' for 6 meters = 0. 01 of 600 meters = .63 feet. 

0° 07' for 1,700 meters : - = 12. 10 feet. 

0° 07' for 50 meters = .34 feet. 

0° 07' for 6 meters = .01 feet. 

Total : •- 107. 37 



In these observations three stations at least should be observed when practicable, and the 
mean adopted. On an instrument at times unavoidably subject to such rough usage as the alidade, 
the adjustment of the vertical arc should be frequently examined. 



30 TREATISE ON THE PLANE-TABLE, 

A material advantage in the attachment of the longitudinal level to the alidade is found in the 
facility by which the instrument may be used as a level in following outlines of equal elevation, 
making it particularly serviceable in this respect on gradually sloping ground. 

A formula for computation of heights, which may prove of service where no table of heights 
is at hand, is appended. 

When a surveyor's level is employed for all elevations, the determination of the position of the 
level pegs by the plane-table on the sheet may be all that is necessary, and the contours may be 
readily traced. The topographer should be careful, however, in this case to determine and sketch 
all irregular accidents of ground. 

Barometric heights are admissible for approximate contours in reconnoissance where a general 
survey only of hills or ranges is expected. 

In using the aneroid barometer in ordinary reconnoissance it will suffice to allow ninety-two 
feet of elevation for every 0. 1 of an inch fall of the index. This allowance is for a mean tempera- 
ture of the two stations of 55° Fahrenheit, and will vary with the temperature. 

Leshe's formula, simple and easily remembered, is a good approximation below 2,000 feet, and 

convenient for aneroid observations, viz: 55,000 X Ty ~ , = height in feet, B being the upper, and b 

the lower, reading of the aneroid. This is likewise for a mean temperature of 55°. 

A very convenient instrument for a tolerably close location of contours, when carefully employed, 
is Locke's hand-level, which can be readily carried in the pocket, it being requisite only to know 
the height of the eye from the ground, and for the observer to stand equally erect at all points of 
observation, or to hold the level at a constant height upon a measured staff. 

Formula for determining heights by a vertical angle and distance. — The difference of level consists 
of two parts, that which arises from the angle of elevation above the horizontal plane of the station, 
and that which is due to the curvature of the earth. The former depends upon the angle and dis- 
tance, the latter upon the distance and the earth's radius. If a' be the angle of elevation in min- 
utes of arc, d the distance, h the height, then, as the tangent of 1' is y^y, we have for the first part 
h= T ^ TT a'd, if h and d are both expressed in the same units of length; but if d is -expressed in 
meters and h in feet, one meter being 3.28 feet, we get h= J J TS a'd. For the fraction j-J^g- we may 
conveniently and with sufficient accuracy put T -^- 0() less -^ of T oVo? an( l thus nn( l * ne rule: 
Multiply the distance in meters ivith the number of minutes of arc, point off the thousandth part, and 
subtract the twentieth part of the number thus obtained. This will give the first portion of difference 
of height, whether elevation or depression. 

The second term, depending on the curvature, varies as the square of the distance, and amounts 
to 0.22 foot in 1,000 meters, including the effect of ordinary refraction. As with the instruments 
under consideration extreme accuracy is not attainable, it is plain that for distances under 1,000 
meters this term maybe neglected. When the distance is greater we have the following rule: 
Talce the thousandth part of the distance in meters, square the same, having regard to the first decimal 
figure, and multiply by 0.22. This term is always positive; if the first term be an elevation, it is 
Increased; if a depression it is diminished by the second term. 

Example. — Distance = 5,500 meters; angle of elevation, 36'. . 

TT ^d!xa / = 198.000 T ^d = 5.5 

subtract-^ 9.9 square =30.2 

multiply by 0.22 

first term 188.1 



second term 0.6 second term G.64 



sum 194.7 = difference of elevation in feet. 



AND ITS USE IN TOPOGKAPHICAL SURVEYING. 



31 



The above formula is near enough for distances up to ten and fifteen miles, and will not differ 
by as much as a foot from the result of a rigorous formula ; in fact, it "will keep within the limits of 
uncertainty of the refraction itself. 

Table showing the height in feet corresponding to a given angle of elevation and a given distance in meters. 



Meters. 


300 


400 


500 


600 


700 


800 


900 


1,000 


1,100 


1,200 


1,300 


1,400 


1,500 


1,600 


1,700 


1,800 


1,900 


2,000 


Angle. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


V 


0.3 


0.4 


0.6 


0.6 


0.8 


0.9 


1.0 


1.2 


1.3 


1.5 


1.7 


1.8 


2.0 


2.2 


2.3 


2.5 


2.7 


2.8 


2 


0.6 


0.8 


1.0 


1.2 


1.5 


1.7 


1.9 


2.1 


2.4 


2.6 


2.9 


3.1 


3.4 


3.7 


3.9 


4.2 


4.5 


4.7 


3 


0.9 


1.2 


1.5 


1.8 


2.2 


2.5 


2.8 


3.1 


3.4 


3.8 


4.2 


4.4 


4.8 


5.3 


5.6 


5.9 


6.3 


6.6 


4 


1.2 


1.5 


' 2.0 


2.4 


2.8 


3.2 


3.6 


4.1 


4.5 


4.9 


5.4 


5.8 


6.3 


6.8 


7.2 


7.6 


8.1 


8.6 


5 


1.5 


1.9 


2.4 


2.9 


3.5 


4.0 


4.5 


5.0 


5.5 


6.1 


6.6 


7.1 


7.7 


8.3 


8.8 


9.4 


9.9 


10.5 


6 


1.8 


2.3 


2.9 


3.5 


4.2 


4.8 


5.3 


5.9 


6.6 


7.2 


7.9 


8.5 


9.1 


9.8 


10.4 


11.1 


11.7 


12.4 


7 


2.1 


2.7 


3.4 


4.1 


4.8 


5.5 


6.2 


6.9 


7.6 


8.4 


9.1 


9.8 


10.6 


11.4 


12.1 


12.8 


13.5 


14.3 


8 


2.4 


3.1 


3.9 


4.6 


5. 5 


6.3 


7.1 


7.9 


8.7 


9.5 


10.4 


11.1 


12.0 


12.9 


13.7 


14.5 


15.3 


16.2 


9 


2.7 


3.5 


4.4 


5.2 


6.2 


7.0 


7.9 


8.8 


9.7 


10.7 


11.6 


12.5 


13.4 


14.4 


15.3 


16.2 


17.2 


18.1 


10 


2.9 


3.8 


4.9 


5.8 


6.8 


7.8 


8.8 


9.8 


10.8 


11.8 


12.8 


13.8 


14.9 


15.9 


16.9 


17.9 


19.0 


20.0 


11 


3.2 


4.2 


5.3 


6.4 


7.5 


8.6 


9.6 


10.7 


11.8 


13.0 


14.1 


15.1 


16.3 


17.5 


18.6 


19.7 


20.8 


21.9 


12 


3.5 


4.6 


5.8 


6.9 


8.2 


9.3 


10.5 


11.7 


12.9 


14.1 


15.3 


16.5 


17.7 


19.0 


20.2 


21.4 


22.6 


23.8 


13 


3.8 


5.0 


6.3 


7.5 


8.8 


10.1 


11.4 


12.6 


13.9 


15.2 


16.6 


17.8 


19.2 


20.5 


21.-8 


23.1 


24.4 


25.7 


14 


4.1 


5.4 


6.8 


8.1 


9.5 


10.9 


12.2 


13.6 


15.0 


16.4 


17.8 


19.1 


20.6 


22.0 


23.4 


24.8 


26.2 


27.6 


15 


4.4 


5.7 


7.2 


8.6 


10.2 


11.6 


13.1 


14.5 


16.0 


17.5 


19.0 


20.5 


22.0 


23.6 


25.0 


26.5 


28.0 


29.5 


16 


4.7 


6.1 


7.7 


9.2 


10.8 


12.4 


13.9 


15.5 


17.1 


18.7 


20.3 


21.8 


23.5 


25.1 


26.7 


28.2 


29.9 


31.4 


17 


4.9 


6.5 


8.2 


9.8 


11.5 


13.1 


14.8 


16.5 


18.1 


19.8 


21.5 


23.1 


24.9 


26.6 


28.3 


30.0 


31.7 


33.4 


18 


5.2 


6.9 


8.7 


10.4 


12.2 


13.9 


15.7 


17.4 


19.2 


21.0 


22.8 


24.5 


26.3 


28.2 


29.9 


31.7 


33.5 


35.3 


19 


5.5 


7.3 


9.1 


10.9 


12.8 


14.7 


16.5 


18.4 


20.2 


22.1 


24.0 


25.8 


27.7 


29.7 


31.5 


33.4 


35.3 


37.2 


20 


5.8 


7.7 


9.6 


11.5 


13.5 


15.4 


. 17.4 


19.3 


21.3 


23.3 


25.2 


27.2 


29.2 


31.2 


33.2 


35.1 


37.1 


39.1 


21 


6.1 


8.0 


10.1 


12.1 


14.2 


16.2 


18.2 


20.3 


22.3 


24.4 


26.5 


28.5 


30.6 


32.7 


34.8 


36.8 


38.9 


41.0 


22 


6.4 


8.4 


10.6 


12.6 


14.9 


17.0 


19.1 


21.2 


23.4 


25.5 


27.7 


29.8 


32.0 


34.3 


36.4 


38.5 


40.7 


42.9 


23 


6.7 


8.8 


11.1 


13.2 


15.5 


17.7 


20.0 


22.2 


24.4 


26.7 


29.0 


31.2 


33.5 


35.8 


38.0 


40.3 


42.5 


44.8 


24 


6.9 


9.2 


11.5 


13.8 


16.2 


18.5 


20.8 


23.1 


25.5 


27.8 


30.2 


32.5 


34.9 


37.3 


39.6 


42.0 


44.3 


46.7 


25 


7.2 


9.6 


12.0 


14.4 


16.9 


19.3 


21.7 


24.1 


26.5 


29.0 


31.4 


33.8 


36.3 


38.8 


41.3 


43.7 


46.2 


48.6 


26 


7.5 


9.9 


12.5 


14.9 


17.5 


20.0 


22.5 


25.0 


27.6 


30.1 


32.7 


35.2 


37.8 


40.4 


42.9 


45.4 


48.0 


50.5 


2* 


7.8 


10.3 


13.0 


15.5 


18.2 


20.8 


23.4 


26.0 


28.6 


31.3 


33.9 


36.5 


39.2 


41.9 


44.5 


47.1 


49.8 


52.4 


28 


8.1 


10.7 


13.4 


16.1 


18.9 


21.5 


24.2 


26.9 


29.7 


32.4 


35.2 


37.8 


40.6 


43.4 


46.1 


48.8 


51.6 


54.3 


29 


8.4 


11.1 


13.9 


16.7 


19.5 


22.3 


25.1 


27.9 


30.7 


33.6 


36.4 


39.2 


42.1 


45.0 


47.8 


50.6 


53. 4 


56.2 


30 


8.7 


11.5 


14.4 


17.2 


20.2 


23.1 


20.0 


28.9 


31.8 


34.7 


37.6 


40.5 


43.5 


46.5 


49.4 


52.3 


55.2 


58.2 


40 


11.5 


15.3 


19.2 


22.9 


26.9 


30.7 


34.6 


38.4 


42.3 


46.1 


50.0 


53.9 


- 57.8 


61.7 


65.6 


69.4 


73. J 


77.3 


50 


14.4 


19.1 


23.9 


28.7 


33.5 


38.3 


43.2 


47.9 


52.7 


57.6 


62.4 


67.2 


72.1 


77.0 


81.8 


86.6 


91.5 


96.3 


1° 00 


17.2 


22.9 


28.7 


34.4 


40.2 


46.0 


51.7 


57.5 


63.3 


69.0 


74.8 


80.6 


86.4 


92.3 


98.0 


104 


110 


115 


1 10 


20.1 


26.7 


36.5 


40.1 


46.9 


53.6 


60.3 


67.0 


73.8 


80.5 


87.2 


93.9 


100.7 


107.5 


114.3 


121 


128 


134 


1 20 


23.0 


30.5 


38.3 


45.8 


53.6 


61.2 


69.0 


76.6 


84.2 


91.9 


99.6 


107.3 


115.1 


123 


131 


138 


146 


154 


1 30 


25.8 


34.4 


43.0 


51.6 


60.3 


69.0 


77.7 


86.1 


94.7 


103.4 


112.0 


120.7 


130 


138 


147 


155 


164 


173 


1 40 


28.7 


38.2 


47.8 


57.3 


66.9 


76.6 


86.3 


95.6 


105.2 


115 


124 


134 


144 


153 


163 


173 


182 


192 


1 50 


31.6 


42.0 


52.6 


63 


73.6 


84.2 


94.9 


105.2 


115.7 


126 


137 


147 


158 


169 


179 


190 


200 


211 


2 00 


34.4 


45.8 


57.4 


68.9 


80 


92 


103 


115 


126 


138 


149 


161 


172 


184 


195 


207 


218 


230 


2 30 


43.0 


57.3 


71.7 


86.0 


100 


115 


129 


144 


158 


172 


186 


201 


215 


230 


244 


259 


273 


287 


3 00 


51.6 


68.8 


86.2 


103.2 


120 


138 


155 


172 


190 


207 


224 


241 


259 


276 


293 


310 


328 


345 


3 30 


60.2 


80.4 


100.5 


120.5 


141 


161 


181 


201 


221 


241 


261 


281 


302 


322 


342 


362 


382 


402 


4 00 


68.9 


91.8 


114.8 


137.7 


16L 


184 


207 


230 


253 


276 


299 


322 


345 


368 


391 


414 


437 


460 



CHAIN. 



As the circumstances under which the use of the chain is necessary are mentioned elsewhere, 
it is only requisite to give a short description of the one employed in the Coast Survey. It is 



32 TKEATISE ON THE PLANE-TABLE, 

twenty meters long, and consists of that number of pieces of stout iron or steel wire, exactly one 
meter in length, each end of which is bent into an eye, and connected by a ring with the eye of the 
following link. For convenience of carriage these links are subdivided in some chains ; but the 
advantage resulting from this is questionable, as the rupture almost invariably occurs at the joints, 
and multiplying them increases the liability to breakage; besides, the "kinking," or tendency to 
overlap or double, is also increased in proportion to the number of joints. On the other hand, it 
may be said that the bending of the links is decreased in proportion to their shortness. 

At each extremity of the chain is a large ring, which slips over a staff held in the hand of the 
chainman, and rests upon a projecting rim of the pointed iron shoe at its base. The centers of 
these rings at the ends of the extended chain are the extremities of a line of twenty meters, and 
the points at which the pins shoidd be inserted during the chaining. 

As the strain constantly exerted upon the chain to straighten it must finally lengthen it by the 
" giving" of the rings, or as it may at times be shortened when the links are bent by being drawn 
over fences, rocks, or other unyielding obstructions, it is well to test its length occasionally. Im- 
portant errors have arisen where dependence has been placed entirely upon long chained distances 
from a neglect of this source of error. 

Adjusting screws are attached to the terminal rings of some of the chains, by which any error of 
length can be corrected. 

Each chain is accompanied by the usual number of pins, and a spring wire triangle for carry- 
ing them. The pins are also made of stout wire, about 18 inches long, pointed at one end, and 
bent into a ring at the other. It is well to attach white cotton or red flannel rags to the ring of 
each pin, that the rear chainman may distinguish it more readily in high grass, marsh, bushes, &c, 
and also at the ends of the five, ten, and fifteen meter links of the chain, for facility in counting. 
These rags shoidd be renewed when they become soiled. 

Care shoidd be exercised in the selection of intelligent chainmeu, since it is often upon the pre- 
cision of their work that the correctness of the survey in a great measure depends, and it is not 
always convenient or practicable for an assistant to accompany them. The better man of the two 
should be placed at the rear end of the chain, as he is the more responsible, and the forward man 
should implicitly obey his instructions. In all important places, however, such as closely settled 
districts, villages, and towns, in the measurement of base lines or distances upon which anything 
of special importance may depend, an aid should go with the chain and check the records of the 
men. 

When chaining is done in connection with the plane-table and the station is reached, the chain 
should be drawn sufficiently beyond and clear of the table to be out of the way, so that if more 
chaining is contemplated it does not have to pass the legs of the instrument. 

With the class of young men usually employed as chainmeu in the Coast Survey parties, it has 
been found safe and serviceable, after a little experience, in the absence of an aid, to have the rear 
man keep a chain-book, in which he notes all the crossings of high and low water, intersections of 
brooks, fences, roads, &c, with rectangular offsets to all reasonably accessible points on either 
hand, including bottom and tops of slopes, the record of tallies, and such other matters as may be 
needed,' and may serve to assure accuracy in case of unfavorable intersections. 

It is the habit with some, in obtaining short distances to comparatively unimportant objects, 
to resort to pacing, and practice enables one to ascertain thus the distances sufficiently close for 
plotting on a jooo~o sca l e > hut these distances should never be great, and the topographer should 
be well assured of the accuracy of the pace. The use of the telemeter, however, may take the 
place of this method. # 



AND ITS USE IN TOPOGRAPHICAL SURVEYING. 33 

All distances to objects on either side of the chain line should be taken by offsets at right 
angles to it, and the book of the aid should, as far as possible, be so held that the line drawn as 
his guide in sketching should be in the same direction as the chained line itself, the better to enable 
him to draw his objects in their true relative positions. 

Where great accuracy is necessary, the length of a gradual slope may be measured and the 
angle of inclination taken with the vertical arc, with repetitions, and the measurement made 
reduced to the horizon by means of the following formula : 

Let y be the length of the line measured upon the slope, S its angle of inclination, and its length 

reduced to the horizon ; then — 

x =y cos d. 

6 
The excess of y over x may be computed by the formula, y — x=2y sm 2 -& 

On very large scales, when parts of a meter are perceptible, Payne's tape, consisting of a 
narrow steel ribbon, which can be marked for minute distances, has been employed with advantage. 
It is convenient, also, for rapid reconnaissance in military surveys, and has been used under fire 
almost at double-quick. Under these circumstances three men were employed, the usual back and 
forward chainmen, with another to stand by the pins when stuck until about half the chain had 
passed, then by pointing to indicate the position of the pin to the back chainman, and run forward 
in time to find, without difficulty, the forward pin, and also to change the pins at each tally. This 
tape will not stand as rough handling as the chain, and cannot be repaired in the field when broken, 
while the latter can lose one or more of its links and still be of service. The easy obliteration by 
attrition of the marks measured upon it has also been found a source of difficulty. All things con- 
sidered, however, it is a very useful, compact, and handy instrument. 

TELEMETER. 

In consequence of some of the disadvantages resulting from the employment of the chain, 
among which are the necessity of frequent dependence for correct distances upon the chainmen, the 
number of persons required, the time consumed in its management, and the impediments to its use 
found in the features of some sections of country, another instrument, styled the telemeter, has 
been advantageously introduced in the topographical work of the Coast Survey. 

It appears that instruments of this class were at first generally regarded by scientific men as 
merely ingenious inventions, and not as valuable in most respects as the ordinary method of chain- 
ing, the filling in of details forming a principal exception. From the experience of its use by the 
officers of the Coast Survey, however, it has been satisfactorily ascertained that the rapidity with 
which the details of a survey can be determined and sketched by its use, the smaller number of men 
necessary to be employed, the advantage that the topographer observes the distance without depend- 
ing upon the correctness of others, and the facility with which it may be used in places where the use 
of the chain is impracticable, or at best difficult, render the telemeter a very important acquisition. 
It is not presumed that it will ever entirely supersede the chain as a measuring instrument, but it 
is undoubtedly a facile and useful substitute under certain conditions. 

The telemeter, as used in the Coast Survey, is simply a scale of equal parts, painted upon a 
wooden rod about 10 feet long, 5 inches wide, and 1J inch thick, so graduated that the number 
of divisions upon it, as seen between the upper and lower horizontal wires of the telescope, is 
equal to the number of units in the distance between the observer's eye and the rod held at right 
angles to the line of sight. 

In all cases the telemeter should be graduated experimentally for the particular instrument 
and eye of the observer who has it in use. 
A 22^-5 



34 



TREATISE ON THE PLANE-TABLE, 



The horizontal wires in the diaphragm of the telescope should he accurately adjusted, 
and the divisions of the telemeter made to correspond in length with the distance 
included between the upper and lower wires of the telescope at a carefully measured 
distance, and then divided into as many equal parts as there are units in the distance 
measured. 

For convenience of transportation it can be hinged in the middle, and secured on 
the side when in use by a sliding bolt ; and as it is necessary, when observed upon, that it 
^ should be held accurately at right angles to the line of sight, a small brass moveable 
bar, with sights or a groove upon its upper edge, should be fixed upon the side of the 
rod at a convenient height for the eye of the rodman, and which, when in position, will 
be perpendicular to the plane of the telemeter and directly in the line of sight of the 
telescope. 

The correctness of the telemeter depends upon the closeness of the reading, and the 
accuracy with which the rod is held perpendicularly to the line of sight. 

With ordinary care an error of reading should not occur even at the greatest dis- 
tance denoted on the rod. With the observations carefully made, and the reading of 
the rod reduced to a horizontal plane, the greatest distance given by it — as usually 
divided — can be relied on as practically correct. There is no sensible error at any dis- 
tance greater than 20 meters and less than 260, and, generally speaking, the telescopes 
^ of the Coast Survey alidades have not sufficient reading power beyond 400 meters, but 
it will generally be safe to rely upon it for any distance from 15 to 300 metres, beyond 
which it cannot be read with accuracy for use in constructing a map on a scale of xo^oo* 

The telemeter has been recommended for use in a great variety of cases where it 
becomes necessary to determine distances, in such close filling in as the corners of 
I streets, wharves, &c, determination of all classes of detail, in traverse, shore line, and 
\^ ^^ even the establishment of positions; but in the latter it is safe only to depend upon 
^-^_J good intersections. It has been employed, however, in all manner of detail, and is pre- 
ferred by some to the chain in all cases save in compactly built streets and on long lines, where 
the distances are so great that the telescope will not admit of the accurate reading of the rod; it 
is maintained by some that where only a single point is to be seen positions can be readily and 
accurately determined. 

For the reduction of the hypothenuse to the base, the following table is given: 



Table for reduction of hypothenuse to base. 





Hypothenuse. 


Angle. 














100 meters. 


200 meters. 


300 meters. 


400 meters. 


500 meters. 


5° 


99.62 


199. 24 


298. 86 


398. 48 


498.10 


10° 


98.48 


196. 96 


295. 44 


393. 92 


492. 40 


15° 


96.59 


193. 19 


289. 78 


386. 37 


482. 96 


20° 


93.97 


187. 94 


281. 91 


375. 88 


469. 85 


25° 


90.63 


181. 26 


271. 89 


362. 52 


453. 15 


30° 


86.60 


173. 21 


259. 81 


346. 41 


433. 01 


35° 


81.92 


163. 83 


245. 75 


327. 66 


409. 58 


40° 


76.60 


153. 21 


229. 81 


306. 42 


383. 02 


45° 


70.71 


141.42 


212. 13 


282. 84 


353. 55 



AND ITS USE IN TOPOGEAPHICAL SURVEYING. 35 

RECONNAISSANCE. 

The term reconnaissance as applied to topography is a somewhat indefinite one, or rather it 
might be said it is very comprehensive. When there is any deviation from the closest attainable 
accuracy in a finished plane-table sheet, it becomes, strictly speaking, a reconnaissance map ; and 
the rudest sketch of a country in which the features are delineated in rough approximation, which 
for certain temporary purposes is all that is needed, is likewise so called ; so that in executing this 
kind of work with the plane-table there is much left to the judgment of the topographer. The 
amount of accuracy and closeness of detail required depends solely upon the object for which the 
survey is undertaken, and the time and expense allotted to its execution. It is always best, how- 
ever, to strive for the greatest precision which the circumstances will allow, particularly as the 
sheet may at some future time become available for more important uses than that originally 
intended. 

To the practical surveyor it is unnecessary to give any rules for his guidance, as his knowledge 
of the plane-table and of the requirements of the special work which he is called upon to perform 
will enable him to execute it promptly and satisfactorily. To the beginner, however, a few words 
on this subject, together with a statement of some of the residts of the work accomplished by the 
Coast Survey officers, may not come amiss. 

The recent war has shown in a forcible manner how little accurate information there was with 
respect to the topography of the interior of many of our middle and southern States, and the 
demand for an increased number of topographers in the army was supplied, in answer to the calls 
of the War Department and various generals in the field, from the Coast Survey; and in almost 
every field of operations from the commencement of the war to its close, the plane-table was used. 

Until this time very little use was made in this country of the plane-table as a recounoitering 
instrument, and it is the testimony of all the officers of these parties, as the result of their labors, 
that for rapidity and accuracy in the execution of military reconnaissance it is more effective than 
any other instrument at present used. 

The usual system adopted, in default of triangulation, was the measurement of a base with an 
ordinary chain and triangulating with the plane-table. 

In detailed surveys for the army, where a topographer averages about a square mile a day, a 
chained base of from one-half to three-quarters of a mile for the survey of an area of twenty-five 
square miles is found sufficient. 

At Chattanooga, from two different bases of about half a mile each, plotted on separate sheets, 
and measured once carefully with the common twenty-meters chain, the same chain being used for 
both measurements, after considerable intermediate plane-table triangulation carried on by two 
officers, two objects were determined two and a half miles apart, common to both sheets, which 
were on a scale of 10 ^ 00 , and the discrepancy was but about fifteen meters. Many other points of 
junction iudicated this to be the maximum error. In this case the leaves were mostly off the trees, 
and the hills afforded good points. The sheets covered about twenty square miles each. At 
Nashville there was a discrepancy of about ten meters in two miles. This would be too much 
error for finished work, but it is very accurate under the circumstances. 

At other times, when the character of the country or the pressure of time did not admit of the 
measurement of a preliminary base and topographical triangulation, the work was commenced by 
starting from a single point, and prosecuted by linear measurement with the chain, intersections 
from the ends of the chained lines being taken to determine objects, which, as the work pro- 
gressed, could also be used as checks upon the chaining. Where circumstances permitted, an 
occasional return with the chain to a back point, either to close a series of lines upon it or to start 



36 TREATISE ON THE PLANE-TABLE, 

afresh, was resorted to. This work was generally carried on over roads, and the interior filled in 
by intersections and sketching, as far as practicable. Some of the tests in this latter work, where 
the operations of two officers joined, were remarkably satisfactory. 

It is estimated that with the usual number of hands and a good sketcher for aid, in a country 
of average variety of detail, in which all the houses, prominent barns and out-buildings, streams, 
roads, general outline of woods, and approximate twenty-feet contours are to be shown, on a scale 
of yo Joo? an area °f between two and three square miles can be filled in daily, with not only suffi- 
cient accuracy for military purposes, but so that a trained eye would not discover any marked 
discrepancy between the representation and reality. This rapidity of work, however, could not be 
expected in or near towns or populous districts. It is doubtful if the average work would reach 
more thau one-half this amount. 

In some thickly wooded sections, and where time is limited, it has been found advisable to run 
the main roads with the plane-table, and fill in with the compass, which is more rapid but less 
accurate than where the work is done with the plane-table alone. The usual method employed, 
where these instruments were combined, was as follows : Where the army was stationary, or mov- 
ing leisurely, one main road was run with the plane-table, the topographer being accompanied by 
assistants well practiced in the use of the compass. Upon arriving at any important road or water- 
course, an assistant was sent to the right and left, starting from a plane-table point, determined by 
the chaining, and running as far as was requisite and then returning to the main road again to 
repeat the operation, the compass notes being kept in a book prepared for the purpose. Prominent 
points determined by the plane-table were used as checks in the compass work. The intervening 
topography, where no compass or plane-table work had been done, was sketched in by the chief of 
the party, in which accurate pacing became of great service. 

OFFICE WORK. 

All the drawing of the topographical features of a survey upon the chart should be penciled in 
the field, while they are still under the eye. Sketching and plotting in the office from notes, unless 
the country be near at hand for ready reference in case of doubt or a defective sketch, is objection- 
able. Where this is unavoidable the sketch should be transferred to the sheet as soon as possible 
after having been made, while it is fresh in the mind of the person by whom it was made, and by 
whom also, if possible, it should be plotted. Days which, from inclemency of the weather, are 
unfavorable for out-of-door work, should be allotted to this purpose, and advantage should be taken 
of them, also, for retouching any details of the sheet which may have become indistinct, as it is 
very important that they should not be left indefinite or become obliterated; for when the inking 
is done, as it generally is, at a distance from the field of operations, the necessity for this care is 
obvious. IsTos. 4 and 5 pencils are good for this purpose, for which very hard or very soft and black 
pencils are equally unsuited. 

In the inking of a topographical sheet three requisites to its proper appearance when finished 
should be borne in mind: clearness, neatness, and uniformity. 

The lines and objects should be clean and sharply defined, nothing being left obscure or doubt- 
ful; the paper should be kept unsoiled, and erasures avoided as far as possible, and the style and 
strength of the drawing should be the same throughout. It is an important matter that an easy 
and natural appearance should be given to the map, for, as before remarked, a mere rigid adher- 
ence to conventional signs is not all that is necessary; while there should be no deviation in this 
respect, at the same time the draughtsman should strive to represent the country. There is a great 
difference with regard to this among topographers. Two equally correct charts of the same section 



AND ITS USE IN TOPOGEAPHICAL SURVEYING. 



37 



of ground, executed by different persons, may be inked, and while one will have a stiff and ungrace- 
ful look, the other will appear artistic and natural, giving at once the impression of a faithful rep- 
resentation of the country surveyed. 

Office work should not be commenced until the field-work is entirely completed, as no inked or 
partially inked chart should ever be used in the field. Sometimes, for the special examination of 
an old survey, or for the insertion of some recent artificial or natural changes, this becomes neces- 
sary. There is always a risk of injuring an inked map by exposure to the weather or by using it 
upon a plane-table. 

The inking should commence with the shore-lines, high and low water. The high-water, or 
shore-line proper, should, in all cases, be full and black, the heaviest lines on the sheet, and in this, 
as in all the rest of the ink work, the lines of the survey should be strictly adhered to, where they 
are distinct records of feature. 

The topography, as drawn in the field is supposed to be correct when the chart is finished, and 
no office amendments or changes are admissible. The low- water line is next drawn, not so full as 
the former, but clear, black, and uniform, consisting of a dotted line for sand and mud, and the 
conventional sign where it is formed by shells, rocks, or coral reefs. 

Grass upon flats, or shoals covered at high tide, have no distinct continuous line to mark their 
limits, each being represented in its proper form and within its area by its conventional sign only, 
but the shape should be well and correctly defined. All objects between high and low water, cov- 
ered at full tide, should be represented less boldly than the rest of the map, but not faintly or 
indefinitely. 

The roads should next be inked, plainly and evenly, with parallel sides, except where the survey 
shows a deviation from the general width. Where a road is fenced the fence should be shown by 
the usual sign, and where there is no inclosure a dotted line should indicate the road-side, and then 
should follow the fences and houses. In drawing the latter, care must be taken that the corners 
and angles exhibit a sharp, clear outline, which adds much to the appearance of the map. 

The general skeleton of the survey being now completed, the contours are drawn with a bold, 
uniform, plain red line, without break, over all the other work, following accurately the full range 
of level of each of the contours on the sheet. 

After this comes the general filling in, by conventional signs, of sand, marsh, grass, cultivation, 
orchards, rocks, hachures, &c. Some practice is needed to execute the sand- work regularly and 
neatly. It should never be hurriedly done, though rapidity in this respect follows practice. The 
lines representing marsh, and the delineation of grass on the fast land, shoidd always run in the 
same direction over the whole sheet, and be parallel to the top of the sheet and the title. The 
appended drawing (Sketch No. 32) gives roughly the conventional signs as adopted by and now 
used in the Coast Survey. 

The most difficult part of the inking for a beginner is the lettering, which now follows, and for 
which samples are given, (Sketch No. 32.) It is expected that every topographer shall have learned 
to draw sufficiently well to ink his sheet in a clear and distinct manner, and letter it with some 
regard to neatness and graphic effect, as the appearance of an otherwise well-inked sheet is some- 
times marred by careless or indifferent lettering. 

The location of the names upon the sheet should be such as not to cover or obliterate any detail 
or feature of the survey, and the letters should be put in neatly and gracefully, and in point of size 
and form according to the specimens furnished. The title should finally follow, with such notes as 
may be necessary to explain any peculiarity of the sheet or survey. This title and lettering should, 
as far as practicable, be so placed that when the sheet is held with the top (usually the north or 




38 TREATISE ON THE PLANE-TABLE, AND ITS USE IN TOPOGRAPHICAL SURVEYING. 

east end of the map) from you it can be easily read ; in other words, as nearly parallel to the top 
or upper end of the sheet as the nature of the work will admit. All names well established and 
recognized in the neighborhood, both general and local, should be collected during the survey, and 
their correct orthography ascertained, and, in case of any doubtful or disputed orthography, a 
report should be given of any traditions or any authorities which may bear upon the subject. 
No illuminated or German text, old English, or what is known as " fancy printing," should be 
indulged in, but a strict adherence to simplicity should be maintained. 

The minutes of the parallels of latitude and meridians of longitude should be marked in figures 
at the upper and right-hand ends, respectively, the degrees on the center parallel and center 
meridian only. 

Where the buoys are determined by the topographer, and their names, colors, numbers, or kind 
are known, they should be lettered upon the map. 

The triangulation points should also be lettered, first being surrounded by a small circle. The 
magnetic meridian should be drawn with a half fleur-de-lis afc its head, and the true meridian, 
where no projection is used, with a full one. 



© 





PLANE TABLE 



/ !.S.( 'oast Survey 



No. 30. 



PL^J 





No. 30. 



PLANE TABLE 



Coast Survey Report /£/>'£ 




Cha*.<kKrA*,I.iti 





H 
















4.1 


D 


E" " 










,'(' 


1^0.9 
& 


5843,3 


-"*"" 


-tt_V :_-=r^-a - fi ---. 














18*0.5/ | 

i 
























C V 

i 


II 












H 










i 


g' 

1M1j6 








H 
2i 


B 


7\ ' " 


K> 


-•=» 


\ 












B 








564£3 
















;J 
























r 


i 


L 










D 


H 












iaz.3 


F 
56<t9 1 






H n 

2.1 W 




E 














E 




Size of' J. 


InLifjuarian She* 


t 





















40 35 



34/ 



4o°33 



i^~ 4i^-^4n 3 | 




Diagram, ilhistratincj the mode of constructiruj 
the Conic Dxyectibn for Plat telahte Work, Scale jq§oo 
Scale of Diagram,, j.< >0 - j )0 



1 ■■' ." ;i§ 








'■'".I ' 




-#< 







-;>'-"" «s 



Fu t . 2 





\ 



Tig. 7 





Tig. !) 




Fie,. 10 




fig- u 




Fig. 12 









,-uj W 



Fig. SI 



■ 



■ . .:. ■ 



22 
















r 




. 



LIBRARY OF CONGRESS 



019 423 889 7 






